losing the mouse pointer/cursor - not the connection

Give this a try: boot into Safe Mode according to How to use safe mode on your Mac and test to see if the problem persists. Reboot normally and test again.

NOTE: Safe Mode boot can take up to 3 - 5 minutes as it's doing the following; 

• Verifies your startup disk and attempts to repair directory issues, if needed

• Loads only required kernel extensions (prevents 3rd party kernel/extensions from loading)

• Prevents Startup Items and Login Items from opening automatically

• Disables user-installed fonts 

• Deletes font caches, kernel cache, and other system cache files

I have seen the mouse pointer disappear at times. Sometimes I can get it back by moving the pointer quickly in circles. However, most times I need to move the invisible pointer to the top of the screen and move it to the top right half. Once I'm sure the invisible pointer should be at the top right half of the screen you need to perform a click action on the top right half of the menubar. Most times this will make the mouse pointer visible again. This trick only works on the top right half of the menubar. For some unknown reason clicking the top left half of the menubar has no affect. I was able to verify this with one of our organization's Macs where the pointer would disappear quite often. I have no idea why the mouse pointer disappears, but it is only something I've seen over the last five years or so.

FYI, these are just user to user forums where others users like yourself will respond if they have information. However, you won't always get an immediate response. Sometimes you may need to wait a day or two before someone responds. Some days there may be hundreds of new posts (and hundreds more of updated posts) in just a single forum category so 20 minutes is just not enough time to expect a response.

I have a 2019 Core i9 16" MacBook Pro and I do NOT see the issues you mentioned.

I am not using a Magic Trackpad with it, just the built-in trackpad, though it is unclear if that is a factor - I am guessing that it is not.

There could be other issues.

Please run Etrecheck and post its full report here. Use the "additional text" button and paste the report into the text box.

I am glad you got it sorted out.

And no wonder this didn’t happen before: Universal Control is a feature introduced in Monterey 12.3 as a beta and became officially released in 12.4.