Recommended Menubar Icon Manager App Compatible with BTT?

I've added too many custom menubar icons to the right side of my screen. This is especially noticeable when in certain apps that have so many menubar icons they spill over to the right (MBP 14" 2022, so have a notch).

I notice BTT has built in a method to hide icons, but my problem is the opposite. I need something like a system tray in Windows that pops out, or some way to see menubar items that get "hidden". There's also an option (very cool) to bring up a menubar context menu, but that's for the "regular" menubar on the left (File, Edit, etc.)

Has anyone tried an app such as Bartender 4, or similar, and did they conflict with BTT in any way?

Bartender is great and usually works fine with BTT. I'd recommend to try the trial version and see whether it fits your needs.