It is indeed possible that iOS and Android would be a challenge (I am not knowledgeable in the subject of mobile app development), but I see you have walked that requirement back.
As for macOS and Windows support (and Linux as well), this is not a problem. If you were to create the application using Python, you would use the pySerial Python package. If you were to create the application using Go, you would use the go.bug.st/serial module. Both are cross-platform, so the same code works for all desktop operating systems. You only need to consider the host platform when building executables for the application. You could even skip that if you have Python/Go installed on the machines, since then you can just execute the source code instead of needing an executable. However, both languages have excellent support for building executables for all platforms (in the case of Python, via PyInstaller, and natively in the case of Go).
I also think you may be overestimating what is actually involved in writing such an application. It should be possible to do in a couple dozen lines of fairly basic code.
Likewise, I think you are severely underestimating what would be required to change the serial numbers of the Nano Every boards. There are some significant challenges to overcome:
- Installing the platform that adds support to Arduino IDE for the ATSAMD11 USB chip on the Nano Every, despite the fact that the toolchain for the original platform has gone missing (details in this topic).
- Figuring out how to modify the complex source code in the platform's core to cause your custom "MuxTO" firmware to produce a USB CDC serial port with a fixed serial number (possible somewhat relevant information here).
- Connecting a suitable debug probe/programmer to the test pads on the bottom of the Nano Every board (see this and this).
It is odd that you brought it up. But anyway it is good that we don't need to think about a solution for the problem as it affects programming (though as you see that problem is fairly easily solved thanks to AVRDUDE being such a feature rich tool).