The state of an entire OS, with all running programs, gets saved. It's more complete than when a laptop/notebook does suspend-to-disk. The emulator saves the CPU registers, the RAM, the disks, the parallel port mode, etc.
The trouble is that a connected terminal is not included in that list.
You keep trying to reinvent terminals with features that already exist to solve a problem that needs to be fixed in the server itself.
I emulate lots of different things. I'll make up an extra-simple case to illustrate the problem.
The guest OS running in the emulator is just a bootable floppy image for testing. All it does is print a counter to the serial port, once per hour. Just after 3 hours it has written 0, 1, 2, 3. At this point I make a snapshot file named 0123.snap and let the software continue running. More numbers get printed. Eventually the terminal is showing 0, 1, 2, 3, 4, 5, 6. I decide that I wish to go back in time, so I issue a command to load the 0123.snap file into the emulator. The internal state of the emulator warps back to the point at which I took the snapshot. The CPU registers, the RAM, and everything else within the emulator are now as they were earlier. The terminal retains the old state however, because it is a separate program with no awareness of the fact that I just loaded the 0123.snap file into my emulator. The guest OS carries on from the original point of course, since that is what the CPU and RAM state dictates, so a "4" will be printed next. The terminal then shows 0, 1, 2, 3, 4, 5, 6, 4. The numbers are simply wrong. They should be 0, 1, 2, 3, 4.
I can only avoid this fate by saving full terminal state whenever I save the emulator state, and of course restoring it at the same time too. There is no reasonable way to extract terminal state from a separate terminal program. (attacking it with ptrace is not reasonable) I thus conclude that the terminal must be built into the emulator.
It's called a "terminal multiplexer" and that is exactly what I suggested with the tmux solution right from the bloody start. I've lost track of how many times I've said this needed to be solved on the server yet you repeatedly pushed back on both points when they were made, insisting it was a terminal emulator issue on the client side.
The serial port is an emulated 16550 chip. It is much more than a PTY. It has clock divider registers, an interrupt cause register, a transmit holding register, etc.
Scroll back buffer history won't let me untype something. If I take a snapshot, then a character is output to the terminal, and then I load that snapshot, the character needs to disappear from the screen. Of course, "character" could be something more destructive, like a scrolling operation or the clearing of a line.
If you disable local echo and have the server side software handle that (like how the SSH protocol works) then it becomes even easier because you then also manage the terminal state (to some degree) via the server as well.
I've written quite a bit of software around this kind of area and I really doesn't sound like a problem that hasn't already largely been solved. I mean if you're feeling really lazy you could just build a terminal server that supports detachable sessions (eg tmux or screen) and that would get around the scroll back issues without you having to write a single line of code.
Like I said, I've done a lot of work with serial interfaces much more archaic than what you've described and have been able to get them working without having to write too much magic. So I suspect you've over thought your problem because it still seems really straightforward to solve from this latest description. Like I said before, terminals literally are just flows of text (ironically there's even less complexity there since you're dealing with serial interfaces rather than PTYs) so all you actually need to do is ensure your terminals output is persistent - which is actually a surprisingly easy job.
