Epson V39 II scanner not connecting to iMac via USB C adapter

Looks like this scanner does not have its own power source, but is bus-powered, and may draw as much power (500mA @ 5V, or 2.5W) as the USB 2.0 specification allows.

If you were plugging this scanner into any sort of hub or dock, I would suggest making sure that the hub had a power source of its own.

If it's just the scanner, a third-party USB-C to USB-A adapter, and the Mac, I'd suspect the third-party adapter wasn't properly transmitting 5V power from one side to another, as unlikely as that might seem to be. (I have a couple of Apple USB-C to USB adapters that I use as needed, and those do provide power to the USB-A side.)

did you install epsons mac driver and software?

Epson Perfection V39 II | Support | Epson US

I don't believe that a driver built for Mojave will work on a 24" M1 iMac running Sonoma.

Old-style drivers often shipped in the form of Intel-only kernel extensions. Apple Silicon Macs can run some Intel application code using Rosetta 2, but they cannot run Intel-only system code such as Intel kernel extensions. On top of that, Apple has been making security changes to recent versions of macOS to deprecate the use of kernel extensions in favor of system extensions that have more limited privileges.

Oddly enough, the Epson site seems to show the same 2025 driver and 2023 combo driver and utilities whether you select Mojave or Sonoma. But hopefully selecting the right OS and then hitting Go before downloading gets you the right one.

it does however let you sellect 10.14.X where X would likely cover all revisions of that macOS version..