I dread this sort of thing happening to me as I don't have the knowledge to correct whatever goes wrong and I just get totally stressed. Hopefully someone can give you good, correct advice.
There should be no need to do so Richard...... but !
I would start by trying the update button for PS v 24.7.2. If no good try the check for updates/Update All options.
If you are still stuck you may have to go the nuclear option.
I had no issues updating to PS v 25.1. One thing I always do when a completely new version comes out (as opposed to an interim update) is to select the option that says "delete previous versions"
No need to remove Photoshop and totally reinstall it. It just looks like you might have missed an update at some point in the past.
The Beta and regular Photoshop install as two totally different products, so no issues there. I have uninstalled my Beta as Firefly has now been rolled out in the standard product.
In general, it makes sense to install the updates in order, but frankly, I have jumped directly into the latest version without installing an older update without any issues in the past with no problems being encountered. I suspect that going directly to 25.1 from where you are will work just fine. If you are concerned, do 24.7.2 first (no harm in that).
A bit off topic, but I too recently deleted the beta version. It's no longer needed for the new AI-based features, and I found it annoying because it often came up from LR when I wanted the regular version and because it was constantly updating.