By "sort my photo albums to alphabetical order by name," are you talking about sorting the albums within a folder, or sorting pictures in an album? I think you mean sorting albums with a folder, is that right? You haven't told us what Mac and OS you are using. Do you have "Optimize Storage" checked? Where is your Photos Library located on your Mac-- in the Pictures folder?
I just tried sorting a folder's albums by name, and it very quickly showed at iCloud.com. I then manually put them in reverse order, and that order automatically copied to iCloud.
Oddly, a couple of weeks ago, the order of pictures in an album in iCloud seemed to refuse to agree with the sorting on my Mac. I re-ordered them manually, and that stuck. (Well, would I know-- I forced them to be ordered the same way as the Mac.)
You should try the usual things-- the things you try when it doesn't make any sense:
- Restart the computer (of course)
- Re-start in Safe Mode. This bypasses certain potentially disruptive processes. 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. The new user will need the same Apple ID.
- [ I usually include "make a new Library," but that would be very messy, in this case. In a sense, we did this when I tried it. ]
- Rebuild your Photos Library--close Photos and re-launch by option-command-clicking the app icon.
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.
Be sure to answer the questions I asked in the first paragraph-- probably before you try anything else. I was using an M3 and Sonoma.