• The M4 shipped with Sequoia. I suspect that it inherited the Sequoia version of Epson's driver when we did Migration Assistant from the M3 to the M4.
Your suspicions are correct. None of that should have been a problem. It sounds completely reasonable. If not for the particular printer model, it's exactly what I've been doing for decades — consistent with what HWTech wrote, for the reasons he explained.
When the M4 wouldn't print we upgraded it and the M3 to Thahoe and installed Epsons MacOS26 diver.
Installed the driver on both the M3 and M4? Not that it matters, it's also completely reasonable. Yet the M3 continues to print whereas the M4 won't.
That brings us back to my suspicion that Epson is missing something with their driver implementation for that specific model Mac. If not for the fact I believe you did it already, you might consider completely erasing the M4 and repopulating its contents from the M3 when offered the opportunity (again). When I start repeating things that should have worked the first time, a course correction is required. In such cases doing anything different is preferable, even if it makes no sense.
Be sure to select "Computer and network settings".
As I wrote I think that is consistent with how you set up that Mac to begin with, and I'm still at a loss to understand what's wrong.
• One thing I noticed but failed to mention is that on the M4 the cupsd process seems to be always running while on our other Macs it only runs when there is a print job pending.
Not surprising since the M4 is sending the print job but it is apparently getting stuck somewhere in the CUPS filter. You can see how CUPS is working by loading http://localhost:631/ in a browser (authentication required). Don't change anything.
Printer sharing is only intended to serve as a troubleshooting step. As a solution it would be an unattractive workaround. There are less unattractive workarounds, but they're still ugly.
For now I can only point fingers at Epson. It's their driver, and I'd want them to demonstrate it works with your specific hardware with its specific macOS version.