Mouse Clicks Not Behaving As Expected

Here's a weird problem that's been making me crazy for two days now.

Here are some symptoms that happen at random when I click on something:

• Unwanted Multi-Select: When I click on a file or folder (say, in Finder) it highlights normally, but when I click something else, the first item remains selected as if holding down the CMD key.
• Unwanted New Tabs: In Finder and in Chrome, clicking an item or a link opens up a new tab, again as if holding down the CMD key.
• Unresponsive Window Selection: clicking on another window fails to select that window, but CMD+TAB works normally, again, as if holding down the CMD key...

The behavior persists for about a minute, then reverts to normal operation for a while, seemingly at random. Pressing the Option key also seems to revert things back to expected behavior.

I'm on a 2023 Mac Studio with an M2 Max chip and 64 GB RAM with about 100 GB free storage. (So no option to reset PRAM or SMC.)

I have tried completely shutting down and rebooting, running in Safe Mode, updating my OS from Sonoma to Sequoia, and even replaced my keyboard, all without any improvement.

It's as if I was holding down the COMMAND key while clicking -- but I'm not. (And it happens with this new keyboard, anyway.)

My Magic Mouse (and the original keyboard) are both about 7-8 years old. The mouse seems to operate normally: no hiccups or glitches, smooth operation, no lag, etc., and a full charge lasts about a month of heavy use.

Has anyone else experienced anything like this? Is it possible that my Magic Mouse is the culprit?