Right Mousepad Button Not Working 22.04 Budgie

The advantage for the user of LTS versions is in their name (Long Time Support): you don’t have to upgrade the system too regularly. For greater peace of mind, there are “rolling” distributions such as, among others, Solus, the originator of the Budgie desktop which update themselves.

The problem with scheduled distributions like Ubuntu is most often the kernel version changes this entails: the previous kernel worked, the next one causes problems (or sometimes vice versa, for that matter).
As it happens, UB 24.04.2 jumped between versions 6.8.0 and 6.11.0. Version 6.8.0 caused a number of problems that 6.11.0 will perhaps solve — unless it creates new ones.

Sometimes it’s enough to go back to the previous kernel, sometimes it’s enough to switch to the next one, which hasn’t yet been adopted by the distribution…

But as @fossfreedom rightly suggests, try with the previous version in the advanced options, that’s the easiest way :