With the version Firefox 109 release, you added this new button without the option to change its position or move into the overflow area. Please let use move it. I can remove/hide almost every other UI element in the browser, why not this?
I read through the most of the responses to this question about why the button can't be hidden and frankly the following works both ways for people who do different things in different ways.
Don't shoot the messenger here I am just telling briefly what I did not to lose it but to get it out of the way, maybe that'll work for some people, obviously depends on your setup.
So anyway I added four spaces in front of the button. It pushed it off to the side where I can pretty much forget about it and certainly not hit it by mistake is many times that I have in the past. Also the hamburger has to stay where it is apparently that cannot be moved.
Try using the Floorp browser this gives this option to hide the Unified Extensions Button, simply go into the Customise Toolbar Settings and at the bottom of the window you will see have the option to hide/unhide this button via the check box.
My Floorp browser is installed on macOS Sequoia, butnthis option should be there in all Floorp browser versions.