I don’t know if others on the latest Tahoe (non beta) have issues with Bartender 6, but it’s been the sole problem I’ve had since the upgrade. Endlessly re-indexing the apps, and slowing the Mac down to a crawl, only fixable by quitting.
In any case, if you are facing similar, I’ve been having no issues at all since switching to Ice, which has all the features I need from such a tool. https://github.com/jordanbaird/Ice
I switched to Barbee, available on the App Store. There’s a short free trial of the full-featured version, and the lifetime subscription is only $13 (it was cheaper a few months ago). Anyway, it’s kept up to date and performs better than Bartender for my needs.
With respect to Ice, I saw after upgrading to Tahoe that the menu bar layout in its settings was blank, and so nothing could be moved, added or hidden. Several others reported the same on GitHub and the developer released a beta (0.11.13-dev.2) that fixes it. The current release (0.11.12) still has the problem.
I was using Barttender 6.04 on my MacBook Pro 16 (M4) under Tahoe, and it was generally (usually) working. However I notice that scrolling in Mail and Safari slowed and became choppy after a while. While restarting fixed the problem, it came back. I discovered that quitting Bartender fixed the problem, so I looked at alternatives.
I am now using Barbee without any significant issues. It was a bit of a learning curve to install and use, but it seems fine.