Tmux drops DCS that it doesn't know like this. That aside, this is extra state per cell that needs to be tracked, handled, understood from a rendering perspective etc. It can work, but would require maybe a thousand lines of code or so to support storing and handling state, redraw etc. and all the various edge cases.
Really? That surprises me. Not saying it’s untrue, just that I’m surprised. I’ve found tmux doesn’t drop CSI, OSC nor APC.
I wouldn’t recommend APC because Apple Terminal doesn’t follow spec with APC parsing (one of the reasons I switched some of my custom sequences from APC to OSC).
Regarding the extra state to be tracked, tmux wouldn’t handle that cell state. That would be down to the terminal emulator.
Since these are cell properties, it does feel like CSI would be the right place (like Kittys undercurl).