There’s some advantages to the manual method. I have done this, and I find that the software mouse shows up as multiple devices with typically an additional serial device for programming.

If you’re doing this for something like a work computer, it’s preferable not to have unusual devices get logged.

Remmina (Linux RDP client) has this builtin (called mouse_jitter), but it doesn't seem to work with more than one simultaneous connections. Still, it's a live saver if the remote system is configured to go into standby when idle.