I see the Private Language argument as the best way to dismiss solipsism, and to establish that truly private experiences are not coherent - though considering non-social adaptively intelligent animals seems to indicate limits to that (in the sense of language as conceptual abstracts, but not in the sense of a shared cognitive/evolutionary space of mutual relatable subjective experience, arguably the substrate of language)
Through being raised as children and enculturated, we establish shared meanings founded in shared modes of life. These are what are important, rather than the private subjective experience. We know a colourblind person sees colours differently, but in most situations they are able use colours in socially appropriate ways. Typical colourblindness (deuteranomaly or red-green type) people only have two types of cone cell active. There are also thought to be some people, women in families prone to that condition, with four active cone cell types, adding additional sensitivity at the red end of the spectrum - it is notable that does not seem to have been picked up socially in an obvious way. Feelings, like colours, are not important primarily for their private qualities, though they initiate instinctive responses like fear-alertness, but are shaped and directed and deepened by being enmeshed in shared modes of life, and collectively socially meaningful only through shared context, whether intuitions we have about bodies like our own or language.
There are 'culturally local' experiences, achieved through their practices, like initiation rights, festivals with a certain state of mind or attitude cultivated, or language structures and associated bodies of stories and literature that exemplify it's scope. There are fundamental limits how far we can truly translate these, it takes somebody with deep experience of not only two languages but two cultures, and even then a description is bound to leave gaps - I am thinking of something like the film The Colour Of Pomegranites https://youtu.be/26tEfblGH5I about lost Armenian culture, which is an amazing work but can only point enigmatically towards fragments.
The Rosetta Stone is a landmark in language translation, opening up the 'dead' scripts of demotic and hieroglyphic Ancient Egyptian. The decipherment of Linear B script for Ancient Greek is another landmark https://en.m.wikipedia.org/wiki/Linear_B#Discovery_and_decipherment We can't know how much is lost in translation, but tomb inscription, tablets recording debts, and political declarations certainly expand our cultural insights.
What is necessary for 'good translations' gives a key insight into possibilities for interspecies communication, I would contend. We can't just map words & concepts, there needs to be enough meshing of modes of life to learn one culture in context, and experience another - typically this is hugely aided by exposure to both languages and cultures in childhood, especially if they are very different. We also need cultural continuity, like between Ancient China and modern China where intermediate texts let us understand objects and concerns in context. The example is maybe clearer in English, where Shakespeare invented at least 15 words many now very commonly used, and many more turns of phrase which might be obscured to a new speaker of the language without access to his work.
Dolphins have been shown to have a very different mode of communication to humans https://upliftconnect.com/dolphins-communicate-holographically This opens up a great deal more scope for interaction, and sharing of modes of life. There are already humans spending substantial amounts of time with wild dolphins, teaching games and use of toys towards building communication. This cymatic method could likely result in a tool for real-time decryption of dolphin communication, and we might expect a cumbersome sending of preset patterns using some kind of computer, or a more sophisticated flexible sending using a direct-brain input like proposed by Neuralink.
That would enable basic exchange of information. Our genes mean we have a lot in common with dolphins emotionally, as fellow mammals, so a lot of extra implicit information could come with body-language and demeanor correlated with signals (we have a substantial grounding in a shared mode of life, similar bodies - cephalopods that be harder, though we think there has been convergence). We might try children with these tools, or by then be able to induce language neuroplasticity in adults. But to really get deeper insights, humans would have to live more fully with dolphins, live like dolphins. Equivalent to gaining cultural continuity. It seems there needs to be a grounding of shared mapping to reality, constituted of theory-of-mind and modes of life including meaning structures. Context in that is what will reveal the nature of another species' emotions, and even then the fidelity will relate to how deeply we can become meshed with that mapping.
Statistical arguments, how early life occurred on Earth, and the development of multicellular life on at least six different occasions suggest complex life is common in the universe, and communicating with aliens will be the truly grand challenge. It might have to involve creating hybrid beings capable of experiencing the modes of life and cultures of both species. It might be that a substantial development track by humans/Earth life would be needed to interact with aliens capable of interstellar travel. Or, there may have been convergence towards similar behaviours and mental structures that allow communication more readily.