full support for logitech mice (without the logitech software) is planned for early next year.
You can already make it work by using the generic devices section in BTT and creating a custom script. Which logitech mouse are you using? (maybe there is already a script you can use)
I have posted one for the MX Master 3 here (not the S version) Support for Logitech MX Master Mice - #8 by Andreas_Hegenberg