My Finder tags are not working in macOS 15.5

do a A SafeBoot Start up your Mac in safe mode - Apple Support will sort many anomalies

Login and test. Reboot as normal and compare your results. Caches get rebuilt automatically.

So the Finder color tags do not stick, right?

Those Finder Tags seem to be at MacOS:MDItemUserTags and MacOS:MDItemFSLabel and some apps might clear them.

exiftool -a -G1 -s '-MDItem*' file.txt 
[MacOS]         MDItemUserTags                  : Red, Green, Blue
[MacOS]         MDItemFSLabel                   : 4 (Blue)
[...]

Rather than downgrade I'd try to find the cause for that. An EtreCheck report would eliminate much guesswork:

Using EtreCheck to Troubleshoot Potential… - Apple Community

I use tags to organize files and they still work in the files I created before Sequoia. However, I cannot add new tags to any files - new or old - as they disappear as soon as I click away from that file. So "grandfathered" tags are still visible and searchable, I just cannot add a tag to any file.

This isn't new tags either. Even tags that are working on old files cannot be added to any file that didn't have it before Sequoia.

ETA: I just relaunched Finder (as mentioned elsewhere in this thread) and I was able to add a tag. I'll update if this doesn't hold.

Ensure that the Finder tags are fully enabled in Finder > Settings > Tags. By "fully enabled" I mean that the right-column boxes are all checked as shown here:

And if it is a standalone file(s) in the Finder, select the File, right-click and choose the Tags… menu item. Then you can assign one or more tags as appropriate to the file(s).

I am using macOS Sequoia v15.5 and I have no issue assigning, editing, or removing entirely the defined Tags on a file using the previous paragraph approach. Apple's Save/Save As panels allow tag assignment too. I have no issue with Spotlight finding tagged files… including those with multiple assigned tags:

kind:pdf AND (tag:active OR tag:unique OR tag:pdf/a)

Right-click on any tagged file and from the contextual menu, click Tags… That will show any tag on the file. Click additional tags and they will be added behind the existing shown tag(s). When done, press return to save your additional tags and close that contextual window. You can then see the added tags on the file icon, or by a Finder Get Info.