As it stands, the Carrack is the only non-capital ship with a medbay, and the Kraken is a capital ship without a medbay. Why don't more multi-crew ships have medbays of any tier whatsoever?

I'm pretty sure the Kraken will end up with one when we actually put it into production; that was almost certainly just an oversight at the concept stage. I don't think the Carrack is the only non-capital ship with a medbay, because we have the Apollo and the Cutlass Red. I guess it's a bit vague what you call a medbay versus what you call a med bed, the different tiers of med beds. But it's certainly not intentional that just those three ships in the game are only ever going to have them. But it is a supremely powerful feature to have in your ship. So we don't want every ship under the sun having a med bed in there that you have as your mobile respawn point. We do want to restrict the availability of those to ships that make sense. So the Kraken would make sense because it is sort of like a mobile space station. The Carrack is a supremely long-distance exploration ship where you're going to be out in deep, expansive space a long time. But having it in the back of your bog-standard Cutlass that you just chucked in there, maybe not. But the Red, again, is designed as an ambulance. And I think we've shown sneak previews of things like the med gun as well; there will be other ways to heal yourself beyond a med bed going forward. So you won't need a med bed in the back of your ship if you break your legs on a planet. You'll be able to use other mechanics to heal yourself. But med beds will be primarily for the whole respawning aspect.

Doesn't the 890 Jump have one?

The 890, yeah, it has one, but I guess the question was about sub-capital ships having them. Capitals tend to, because again, by their nature and size, they're often long-distance, long-duration.