Quantum indeterminacy is inextricable from observation because that which we consider to be "quantum indeterminacy" is related to the interpretations of QM rather than the mathematical model behind QM.
(I expect this question to get migrated to Physics.SE, because it is really more of a physics question than a philosophy question. When it gets there, I know it will be seen by those who want technical accuracy. This answer is written from a very high level perspective to tie into the more philosophical aspects of QM. Please forgive any technical errors which arise from this process)
When you really get down to it, QM is a model. Its a set of mathematical equations which someone argues describes the behavior of something in the real world. These mathematical equations are very well specified in the unyielding language of mathematics. If you can set up an experiment in the language of this mathematical model, everyone will reach a consensus as to what the result of the experiment will be (also in the language of this mathematical model). The tricky part is in attaching real life meanings to these mathematical devices.
Consider a classical example first. Take the model x=1/2*a*t^2 + v_0^*t + x_0, which we will call a "kinematic model." Everyone will agree that if you take a=2, t=3, v_0=1, and x_0=0, the model will predict that x=12. That's easy. But what does it mean to say x=12. That's the interpretation part of the problem. Once I say that "a is the acceleration of an object," "t is how long the object moves," "v_0 is the initial velocity of the object," and "x_0 is the initial position of the object", I can claim "x is the final position of the object." Until I add that interpretation, it's simply math. Once the interpretation is added, it becomes a model of the physical world around us which can be tested.
So what's an "initial velocity of an object?" That's a lot of words. To describe what I mean, I'll need other words. We'll have to come to agree on a meaning of velocity, for instance. For most of physics, it is assumed that we have a consensus on the meanings of these words, so we use them casually. If I'm studying the reentry of a NASA spacecraft, I'll throw around terms like "freespace energy flux" with the assumption that everyone will agree on what that term means.
With QM, it gets harder. The connection between the world we can observe empirically and the mathematics of QM is more strained than it is in other aspects of physics. We talk of things like "measurements," which are very natural concepts on the scale of human empirical interaction, but they don't quite behave intuitively when you get really small. Thus, the scientists have to take more time explaining their interpretations of how we should think of the model's reflection of reality. In fact, the entire concept of indeterminacy arises in the interpretation layer of QM. The underlying wavefunction equations are straight forward deterministic mathematical equations. Its in the application of these mathematical equations that we find the need for indeterminacy. The famous Heisenburg uncertainty principle only applies to a very particular set of states. It just so happens that, when you attempt to apply QM to reality, those states occur over and over and become very important.
One of the challenges QM faced in the early days was captured in four attributes of an interpretation which were desirable. Using Einstein's terms for them, they were:
- Realism - The idea that things objectively exist, even when they're not being measured. If you believe the universe is real, then you believe that you can look at the moon, then look away, and be confident that the moon did not cease to exist the instant you looked away from it. It persists whether or not it is being observed.
- Completeness - An ideal for many is to have a complete interpretation, which means it accounts for everything observable in the physical world. A theory which predicts the exact behavior of everything in the world, except at one central point of the universe where Loki decided what happens would not be complete. Generally speaking, physicists seek completeness.
- Determinism - The idea that there is no randomness built into the model. When you're trying to explain why people should spend a few years learning your theory of how the universe works, they like to know that they're learning something worthwhile. That's easier to argue if your theory is deterministic.
- Local realism (aka Locality) - This is a strange requirement but very important for QM. Local realism is the idea that all of our measurements are measuring something real, and the effects of measurement don't exceed the speed of light. So much suggests that light is a "speed limit" for our universe, that theories which depend on exceeding it are treated with suspicion. This also matters because if your interpretation has a speed limit, it provides a hard and fast guarantee that Loki (this time a hyper-massive black hole, rather than a Norse god) can't influence your results any faster than you can observe Loki's influence yourself.
As things go, they have found it is not possible to map the mathematics of the quantum mechanics model into reality without sacrificing one of these attributes. Something has to go.
The Copenhagen interpretation, by far the most famous, sacrificed determinism. It stated that an observation would cause a "waveform collapse" which turns a superposition of quantum states into a single classical state. Which state it ends up with is defined randomly, using probability theory. Most people's understanding of quantum uncertainty derives from the Copenhagen interpretation because it won the political fight and because enshrined as the most popular interpretation. However, its full of confusion. Every student worth their salt eventually asks "what is an observation anyways?" It seems like a pretty important thing, since it causes waveforms to collapse. It turns out that the naive answers to this question rapidly turn into dead ends. The double-slit experiment series of experiments typically frustrates new students indoctrinated into the Copenhagen interpretation, and they become enamored with this concept of 'uncertainty' until they develop enough math to move beyond this phase.
Other interpretations give up different things. One interpretation is, in my opinion, highly helpful for you in understanding the issues you are exploring: The Many Worlds Interpretation (MWI). MWI is a complete deterministic interpretation, meaning the state of the current universe fully describes the future state of the universe with no uncertainty. How does it accomplish this? It gives up something dear: realism. Under MWI, one cannot say that any object has an objective state which is measurable. Instead, it is assumed that all states are subjective with respect to an observer. In MWI, you cannot say "the moon exists," but must rather say "whether the moon exists is consistent with my observations of whether the moon exists."
By making this sacrifice, rather than determinism, MWI actually makes it much simpler to stick to the actual mathematics. Take Schrodinger's cat. For Copenhagen enthusiasts, this is a very exacting study in word choice. There's nothing in the Copenhagen interpretation which misrepresents what happens in the Schrodinger's cat thought experiment, but most people start to break out into hives at the idea of a cat that is in a superposition of states of both dead and alive (colloquially termed "half alive and half dead," though that is actually not technically precise wording, and leads people astray). Now consider MWI. Like Copenhagen, MWI starts by describing the cat in a superposition of states entangled with the state of the radioactive isotope in the box. However, once the observation happens, instead of having some complicated wave form collapse occur, MWI takes a simpler approach. The cat's state (alive or dead), cannot be talked about objectively. It can only be discussed with respect to the observer. Thus, we say "The cat's state is consistent with the observer's observed state. Iff the cat is alive, we can be certain the observer measured it as alive. Iff the cat is dead, we can be certain the observer measured it as dead." Case closed. It's elegant really... if you can stomach the possibility that the universe may not be "real."
So this is why I say quantum indeterminacy is inextricable from observation. The indeterminacy only comes into the story once one begins to use an interpretation to tie the mathematical model into having empirical meaning in our universe. Different interpretations have different ways of handling this, including some which permit complete determinism in the universe. If you can permit a deterministic interpretation of QM, then indeterminism must be tied into the interpretation, not anything in the mathematics below.
