In principle, yes. However, I have had bad experiences with it under Linux (Ubuntu 22.04 on a Lenovo Thinkpad T14). The mouse can be connected without any problems, but only works for a short time afterwards. Then the connection breaks off, although the device is still shown as connected. I don't know what exactly the problem is (I use the mouse with the Logitech dongle, which works without problems). There are a few bug reports on BlueZ and Logitech mice on GitHub, so it is quite possible that the problem does not occur in distros with more recent versions of BlueZ or the Linux kernel.

Yes, I connect the mouse with Bluetooth and it works wonderfully.

Yes, it's possible

Yes, BT also works.