Uploading a consciousness into a computer and have it remain "you"? That's completely foreign to what we know today. I'm not saying it's categorically impossible; to your point, if a civilization has advanced to the point where the above is ship is feasible, surely they must have picked this up along the way? Maybe, but maybe not. We don't even know if it is possible. But keep a shitload of people alive in space for a long time? Sounds plausible, even if it is enormously difficult.

Find a way to decompose an individual's personality into progressively more granular dimensions of behavior. Model stimulus -> response reactions as transformations. Sample enough responses from each type of behavior, make linear approximations of the transformations until you achieve a 1:1 simulacra, and derive a basis for the response basis. Your human mind will be a matrix representation of the map between the stimulus and response spaces.

As unrealistic as all of that sounds, it still sounds significantly easier to me than uploading (or even interfacing with) a mind.

On the other hand while uploading minds probably has some issues, it involves replicating thing that we can assume resides in physical space, the question remains as to how and whether at all we can measure the internal structure with sufficient accuracy and whether such measurement is nondestructive.

And in the end, problem of somehow interfacing with an mind can mean many things which range from solved issue (when typing this comment counts as "interfacing") to something that for me seems like purely engineering issue (building new neural attached "peripherals" for the brain or emulating existing ones)

For a basic example off the top of my head, consider a hash function. A hash function h : {0, 1}^' --> {0, 1}^n is not actually* injective (it can't be, since the domain is effectively infinite-dimensional and the codomain is finite-dimensional). However, cryptographic security mandates that it should be infeasible to find a preimage message for any digest in the codomain. Moreover messages with very small differences in the domain should be mapped to digests with very large differences in the codomain. This artificial noise and complexity doesn't resemble human reactions whatsoever; it's fairly easy to say two things which will each elicit your regional-specific greeting. In general many human responses have common triggers, and I would further conjecture that you could categorically simplify this further by reducing human responses to broader equivalence classes based on language, geographical region, mood, etc.

This is not to say it isn't challenging. I would expect building a linear approximation of a human mind using input -> output mappings to be extraordinarily difficult. But it's not artificially difficult, like well-designed cryptography. Breaking well-designed cryptography is intended to be, in a mathematical sense, a maximally difficult endeavor - much more difficult than basically anything else you can possibly do in nature.

More to my original point you and I can at least entertain a coherent conversation about building a matrix representation of a human mind using finite stimulus and response spaces. We're in familiar territory, even if it's not ultimately possible or feasible. It's mathematically sound to approach this, given a few well-defined assumptions.

In contrast, I don't know (nor am I confident anyone else knows) how to 1) replicate a human mind via as of yet nonexistent direct brain-interface technology, or 2) how to upload a human mind, using even more nonexistent technology so as to preserve continuity of consciousness. Not only are there rampant unknowns unknowns involved in the engineering efforts entailed here, there are unresolved questions and rampant philosophical disagreements in the fundamental assumptions. We're not in familiar territory here.

I’d say this is an engineering problem, rather than #2, which is philosophical. For #1, all you really need is to measure all brain cells accurately enough, then recreate the whole thing in a simulation. Could probably be achieved with nanobots or very advanced scanners within couple of centuries. Might be acceptable to destroy the original in the process, if it makes it more feasible.

Some (most?) people have a rich internal world which can never be caught by looking at I/O relations.

Also, do you believe that by asking e.g. a person like Albert Einstein a reasonable amount of questions (an amount that a person can answer without getting seriously annoyed or fatigued), you would be able to reconstruct their problem solving skills? Sounds unlikely to me.

That being said I think your second challenge is more interesting. Albert Einstein's achievements are the product of both extreme knowledge/specialization, his experience and his personality. I think you'd likely have to have a "knowledge space" which can be mapped to the human "mind matrices." That does complicate things a fair bit, but in the abstract I think a "vanilla human" could plausibly be seeded with Einstein's personality and as much knowledge as you want.

How do we know that the incomprehensibly weird and advanced minds running our ships and habitats in those unimaginably distant points of space and time won't just decide that virtual smiley faces with our names written on them are close enough to, "it remains you." How do we know they won't one day do a "slightly lossy compression" of the human race?

If you transform rather than duplicate yourself, it doesn't matter if you're still 'human'. What matters is that you're alive and conscious.

We don’t even know where to start replacing our bodies. AI? Genetics? Cybernetics?

I am not sure of this. Even if we pooled the Earth's resources into constructing a generation ship, we still are not sure we are capable of making a ship that is sustainable both socially and technologically.

We do not know if our tech can last hundreds of years. Even if that wasn't the problem, we do not know if we can maintain a self-sustaining environment that lasts hundreds of years. Even if that wasn't the problem, we don't know what failure modes need to be accounted for. Even if that wasn't the problem, we don't know how to keep humans sane on such a journey. It is, after all, unethical to have new humans born on a journey they never signed up for. We do not have the right to determine the fate of our progeny.

An upload to a synthetic medium is perhaps the only sane and ethical way to accomplish this goal.

Add some check processes which periodically restore an old backup and have a conversation to see if the backup agrees to a merge as the moral monitoring system.