Quote

Bitcoin Core may be too?

If you use Bitcoin Core, then you can make any transaction. For example, you can send coins to "OP_DROP <pubkey> OP_CHECKSIG", then you can spend it by pushing "<signature> <message>". And then, you can push bigger things than 80 bytes (as far as I know, up to 520 bytes, but then you can use more tricks to go above that). Also, putting message as a witness is cheaper, because of Segwit.

Quote

Do I understand correctly that there is no such possibility on hardware wallets?

Technically, it is possible. Practically, it could require writing some software for them. And that's another reason why I avoid hardware wallets: they are too limited for me.

Quote

how many characters can approximately contain these 80 bytes?

That means 80 English characters. For other languages, it may be less, but probably between 2 and 4 bytes per character. Also, you can use Unicode to put "<burger><heart><smile><human>" as emoji, then it could make it shorter, because "burger" will take 6 bytes, but some icon would take at most 4 (unless you want to use a combination, for example a "hand" with a "skin tone one").

Quote

(I've once made a thought experiment: if Bitcoin was banned globally, one could replace the current payments with "human-readable" messages like "I want to thank the person X." or the like, with the public key hash encoded in that message. Would be perfectly possible although obviously we would need to change the tx format for efficiency. Of course that wouldn't impress the regulators much, but it's funny to think about it.)

I also thought about that. But then, there is a bigger problem, because you need some way to implement mining. So, I can see two options: hashing each message separately, or implementing a hidden chain. I prefer the second, because then all hashes could be hidden as commitments. Then, the only option to stop that, would require banning all ways of encrypting anything (or pushing any random, non-explained data), which is hard to enforce.