I think that the (unsatisfying) answer is that there's no established standard for how protocol selection works. nip04 and nip44 are completely different types of messages, and it's up to the client how it'll use and/or respond to them.

I guess it's worth also saying, there is no algorithm selection. Nip04 is dead for DMs. It doesn't need to be backward compatible. A user can't know which client another user is on, nor what their capabilities are, nostr is not smart in that way. Most, if not all, operations on nostr are completely stateless.

When a user decides to send a DM to another user, the client must choose the standard for encryption, and message wrapping. Then hope the other user is using a client that implements the same standard, in order to decrypt the message.

Again, remember, DMs don't have a session. Every message derives a new symmetric key. The only metadata that makes a "chat" session is the timestamp, and the public keys of the users.

Kind of. They are standards for encryption, not the direct message itself. You'd be speaking about nip17. Which i've been mis-speaking as nip19.

https://github.com/nostr-protocol/nips/blob/master/17.md

Notice that nip44 IS the standard. again, nip04 is deprecated, and should be treated by clients as such.