Okay, so I have two machines - each of them running Firefox Portable Dev Edition. One was v119, the other might have been v118.
I updated both of them to v127. Afterwards, Computer-A runs fine, but Computer-B gives the "Firefox is already running, but is not responding. The old Firefox process must be closed to open a new window." error if you try to launch it again to open a new window (as opposed to Ctrl+N).
Both of them have "AllowMultipleInstances=true" set. Setting it to False does serve as a workaround to eliminating the error on Computer-B. But given that Computer-A works fine, clearly, this is not be the source of the problem and something else is responsible.
Are there any ideas as to why setting "AllowMultipleInstances=true" causes this error to show up on one machine but not the other?