Tmux doesn't support serial ports.
Personally I live by the maxim "if it can be separated without significant drawbacks, then it should be separate" but GNU tends to see it differently.
USB is a serial BUS, which allows multiple devices; serial ports are single device (if my memory serves).
Originally, you communicated with the computer using a teletype or video terminal connected to a serial port. Whatever you typed went to the computer, and whatever the computer sent back was printed on your terminal screen (or paper in the case of a teletype).
The UNIX (and thus, Linux) command line environment still works this way, except the serial line is virtual.