I bought a Z80-MBC2 homebrew computer

Nice!

@John Doe Thanks, the Z80-MBC2 works fine now in Crostini!

On Reddit I was advised sometimes Chrome OS doesn't immediately recognize some serial devices, but plugging them again may work. Which it does: I retried and Chrome OS nicely detected the card, offering me to access the USB device from Crostini.

The USB-Serial converter dongle has a CP2102, which is a low-cost device. It might be that the converter is unsupported on the systems you're using, but I would not discard a faulty chip.

The converter should be detected even if it is not attached to the board. Maybe you can try to plug it to a Linux computer and see if it pops up—I've used it in the past, and it worked out-of-the-box on Linux.

Another option is to buy (or borrow, just for testing) a FTDI USB-Serial converter, those are of higher quality and more widely supported.

If you plan to play with SBCs for a while, getting a FTDI is worth it.