Quick status update: unfortunately I'm still not completely ready for a public testflight release, but it's getting much closer.
After I released to some very first testers, it became clear that people are using this to build huge menus (look at https://community.folivora.ai/t/btt-floating-menu-running-on-a-touchmonitor/ or at the stuff @Max_Megalon has been building). I didn't fully anticipate this and had to update some parts of the architecture to allow for performant transfer of these big menus (especially because they can be really dynamic and anything can update at any time).
I have now mostly finished the architecture change and am now starting to validate it with some very big menus.