[It's better to use iCloud Photos-- captions, etc, are transferred faithfully.]
Bird ID is not dependent on the transfer. Here is what I see on my Mac:

(This is a scan of a slide that has not been in another Library or in iCloud.]
You don't say if this problem is confined to birds, or do you get IDs of other things, like bobcats?

Like on an iPhone, you have to have the Info Window open in order to get the information:
Use Visual Look Up to learn more about a photo on Mac - Apple Support
Oddly, unlike on an iPhone, I don't see a way to turn this off and on. It can take days after an update to rescan the pictures, but it sounds like it's been a while for you.
To narrow things down, try this:
- Restart the computer (of course)
- Re-start in Safe Mode. This bypasses certain potentially disruptive processes, and it often helps. Safe Mode is different for different computers, so see this:
Start up your Mac in safe mode - Apple Support
- Make a new user and see if the same problem recurs with it. This is a bit harder, because a new user can't access a different user's stuff. You would need to move your Library out of your own user's folder up to the general "Users" folder.
- Use another library if you have one, or make a small test Library with a few pictures in it and see if the same thing happens. You can create a new Library by closing Photos and then option-clicking on the Photos icon.
- Rebuild your Photos Library--close Photos and re-launch by option-command-clicking the app icon. I put this last because, if you use iCloud Photos, this may cause Photos to take a very long time to re-sync, maybe days, depending on the size of your Library.
The idea is to find out if the problem is with the Library, with your account, or with caches and login items, and stuff like that. One of these steps may fix the problem, but their failure to work also helps figure out what's happening.
Let us know what happens…