Why would you get rid of the Logitech 2.4ghz mouse? These are great (well, the gaming mice), absolutely no difference in performance vs wired, no pairing required..
I'd sometimes have to remove the dongle and re-insert it for it to be recognised (again) by the OS. When I used it via bluetooth it would keep failing to connect and need manual deletion from the list of paired devices and re-adding.
Also its dongle seemed to interfere with my wireless Apple keyboard. Not sure but it seemed to correlate a few times.
It's much better with its own dongle, yes, but ... I got sick of the occasional issues. No issues with a wired mouse.
Experience might be different depending on OS. On macOS, my Logitech mouse would regularly forget its settings, forcing me to reload the profile Iād saved in the software.