I downloaded version 4,616 and the "floating_status_item_bar" preset from the link Manage Menubar Status Items · GitBook
The action "Show/hide Menu Bar Icons Left of specific icon" is not hiding any icon:
One thing to make sure: All menubar item management features require BTT to have the screen recording permissions in System Settings
Yes, BTT has screen recording permissions.
Small video to show that nothing happens when I click the arrow
That's strange, this should be working fine. Which version of macOS are you running?
Have you tried selecting an other item to hide?
Yes, I have tried other items to hide and the issue persists.
I am on Macbook Pro 16' M1 Max 32 GB - Ventura 13.6.7 (22G720)
Ah ok, I assume the approach BTT uses only works on macOS 14/15. I'll probably not add compatibility for macOS 13, but I'll make clear that it requires macOS 14.
That's a pity, I can't leave macOS 13.
I bought some moths ago Bartender app, just for hide some status bar icons.
I have quitted the Bartender app for trying this new BTT feature. Monitor Activity confirms that Bartender is not running, but I wonder if having installed this app can interfere with BTT…
Probably not, I know that Bartender uses different approaches on macOS 13, but I have not done any research on that macOS version myself. Unfortunately there is no official API or anything like this, thus this is all reverse engineering & trial & error.
Hope you can implement this new feature for macOS 13.
I love to manage everything with BTT…
This is really unlikely as my main machines are all running 14 or 15, and a feature like this needs a lot of testing. Maybe if it is just a small change it could work, but I assume it would require a whole different technique on macOS 13 ;-(
Ok, running Bartender again 
Anyway, thanks for the explanations!