Mac Photos albums not available for sync with iPad when connected.

So it's something about the Mac, not the iPad. You've eliminated caches and things like that by using Safe Mode. Here's 3 more things to try:

• 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.
• 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 temporarily move your Library out of your own user's Pictuers folder up to the general "Users" folder. Or you could use the new Library you made.
• Rebuild your Photos Library--close Photos and re-launch by option-command-clicking the app icon. If you use iCloud Photos, it’s possible that this will cause a re-sync that lasts long enough to make you nervous.

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…

I'm not sure what's going on. First, you should try these things on the Mac:

• 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 

On your iPad, you should try a forced restart of the iPad:

Force Re-start iPad

This is different from a simple Power Off. For me, the logo appears way after the Power Off notice.

Ventura is a bit older than iOS18, but I don't think it should be necessary to upgrade. You do need to keep up with security upgrades on the Mac, though.

Let us know what happens…

We've known it's not Ventura-- this a a stable OS. It's something in your user account, clearly. Safe Mode eliminated most caches and login items, and that stuff.

Do you have any iCloud services turned on?

Thomas Ernst wrote: …I have iCloud services turned off, for Photos, iCloud Drive, and Mail. Advanced Data Protection is off.

I asked about iCloud because you can't use iCloud and transfer by cable, both. It was worth a shot.

Have you used any Cleaner type apps?

Have you tried using the app Image Capture that's in the Applications menu? It works the same way Photos does, but sometimes it works when some automatic systems don't.