Humans are always looking for the next big thing and since science is everything; much of what humans are amazed by have some basis in science. We aren’t sure if technology will end; but if it does; what will humans strive to achieve in?
To answer this question, we should inquire on the roles of technology. Then we should inquire on the points of absolute sufficiency for these roles. But first, let us take a definition (from Wikipedia):
Technology can be most broadly defined as the entities, both material and immaterial, created by the application of mental and physical effort in order to achieve some value. In this usage, technology refers to tools and machines that may be used to solve real-world problems. It is a far-reaching term that may include simple tools, such as a crowbar or wooden spoon, or more complex machines, such as a space station or particle accelerator. Tools and machines need not be material; virtual technology, such as computer software and business methods, fall under this definition of technology.
Perhaps the most common example of technology is the making and use of tools. This goes way back for humans, with early tools like hammers and later tools like paper. These are essentially instruments of extended function for the body and mind. Hence, one key answer to the question of technology's role appears to be extending the human into its environment.
A more abstract, yet still common, example of technology is science. Here, as with many other aspects of culture, rather than extending the human into the environment, the environment is extended into the human. Specifically, the human is following externally arrived guidelines or methods to achieve an end.
The overarching theme for technology seems to be extension or integration between a being and its environment. As technology grows, ever more of the environment is repurposed toward the will of the being. Taken to the absolute, every part and wave of substance would bend to the will of the animal. Every aspect of energy and matter were working as one unified lifeform.
Still, different configurations presumably exist for the will and control of the system. If humans are the ones running the place, then as long as reproduction were kept reasonable, practically unlimited energy and resources per person could allow a fairly decent quality of life. Assuming full automation of production and other unfun activities, we would be left to find meaning outside of work. Those interested in competition or spotlight could play sports and other games, or produce works of art. Those wanting more social touch might consider role playing and story telling. And those in need of cognition could study philosophy, religion, or history. Basically all the usual leisure activities apply here.
Even with all material needs met, some moral dilemmas could remain, as asked about here.
It crucially depends why you think progress will stop.
Average living standards of an Ancient Roman citizen were not matched again until London in the 1720s. Nuclear war and following nuclear winter, could see something similar to the sack of Rome - what Joseph Tainter calls 'rapid simplification' in his book 'The Collapse of Complex Civilisations'. Tainter associated these with civilisations depleting their resources, then experiencing a shock which there were no longer materials and social-cohesion to adapt to. Quite a plausible outcome in the face of climate change, also. Though these kind of scenarios would reverse technological development, maybe for a very long time, they would be unlikely to end it.
China developed the three technologies Francis Bacon called 'the cornerstones of the modern age': canals with locks, gunpowder, magnetic compasses. Also paper, and the Treasure Ships trade-exploration missions able to reach Africa by the 1420s. The puzzle that the modern age did not then begin there, is called The Needham Question, and the scholarly consensus is that it related to being such a relatively cohesive political unit compared to Europe, where many small wars acted as selection pressures against social conservatism and entrenched power (the death toll of the Three Kingdom War of Ming to Ching dynasty transition in 3rd C AD, was not exceeded until WW2 - it was an era of exceptional technological development). It is possible to imagine an unchallenged global superstate making a decision to prevent technological developments as disruptive, along the lines of the Japanese ending almost all international trade and having two extra centuries of feudalism until modern weaponry arrived. This scenario would see a kind of stasis or stagnation of technological change, but would be unlikely to end it.
I guess you may have something utopian in mind, a kind of maximisation of the agency of minds or species. You could say extend the Kardashev scale to the harnessing of supergiant blackholes, or supernovas, the most energetic phenomena we know of. Or a VonNeumann machine like the obelisks in Asimov's 2001, capable of replicating themselves to face any task. Penrose pictures a future of humans being able to create almost anything needed even from the 'emptiest' parts of space, using fusion of the cosmic dust there to generate matter and energy, another picture of maximising. I don't see how even there technological possibilities could end. In Penrose's Conformal Cyclic Cosmology the final distribution of photons after the last matter evaporates, could shape the initial conditions and maybe even laws of the next cycle, seeing even the end of the universe as not an obstacle.
It's interesting to look at Schumpeter's technological & entrepreneur-driven business cycles of “successive industrial revolutions":
"Typically, a long upswing in a cycle started when a new set of innovations came into general use—as happened with water power, textiles and iron in the late 18th century; steam, rail and steel in the mid-19th century; and electricity, chemicals and the internal-combustion engine at the turn of the 20th century. In turn, each upswing stimulated investment and an expansion of the economy. These long booms eventually petered out as the technologies matured and returns to investors declined with the dwindling number of opportunities. After a period of much slower expansion came the inevitable decline—only to be followed by a wave of fresh innovations which destroyed the old way of doing things and created the conditions for a new upswing." -from The Economist, 'The long cycles of industrial innovation are becoming shorter'
In the absence of technological change, Schumpeter expects competative-equilibrium. A longer cycle we can examine also has that: evolution. And there we find cycles of Punctuated-Equilibrium, boundary-events driven by comets, volcanoes, ice-ages, and so on, where radial-evolution of survivors refill emptied ecological niches.
Change continues. Replicators that replicate more, become more numerous, compounding replication advantages. This is true among memes, as with genes. I don't see any more than temporary stasis, and average-net increase in technology over time as highly likely, given the dynamics of exponential growth.
For goals in the absence of material needs, I would look to play, as the means to explore the apex of the hierarchy of needs, discussed here: Video games as new art
I do not see how technology would end. But that was not your question of course.
So it is hypothetical.
I think that if technological progression ends, this would equate to everything remaining the same.
That is the short answer.
I find it difficult to see any progress at all if there is no technological progress anymore. It would effect daily life in a major way though. Imagine never getting a new flavor anymore of your favorite drink. Life would start to get pretty boring it seems.
An other thought that comes to mind is why/when would this happen. Would it end if we seize to exist? I don't think so, because there are animals that use technology as well. It's rather simple, but it is there. Multiple animals do this as a matter of fact. So this goes out of the window.
Than maybe it would happen if there is nothing to learn anymore. We know everything that there is to be known. I find it hard to imagine that this would happen at all, but if this were to happen it would be in a point far far in the future. However, in this scenario humans will likely not be recognizable anymore because of the time elapsed between now and than (Darwin and all that ...). In addition, the technology has obviously progressed up to this point and allows for additional changes to our species. In this scenario we would have a solution to all our health problems because we know everything right? We would understand everything there is to know about our DNA and the workings of our brain. You may than even conclude that humanity does not exist anymore. We are talking about such a long time in the future that even without technology the human species would have likely evolved into a different species. So basically humanity will do nothing, simply because it does not exist anymore.
That was too much side tracking.
As to what will humans strive to achieve without technological progress I also struggle. Back to the first one I threw out of the window. If we do not exist anymore, than there is nothing to thrive for. The second scenario is a lot harder. If we live in an environment where we already know everything, it would likely be limited to physical performances such as sports or living arts (acting singing) and stuff like that. Since anything else would likely involve some development. And that in turns implies that we did not know everything. Which is not an option by default of the question asked.
I like your question, but I do not like the thoughts that come to my mind. But I stick to the simple version of my answer. If technological progress stops, everything will remain the same.