So, first, We are quickly getting to the edge of my expertise. Just fair warning.
If everything else is working fine, and 'M' is the only broken key, then whatever the issue is, it's likely localized to the immediate area around your black hotswap socket there. If I were trying to repair this myself, here's what I would try:
Per my annotated pic, use a jumper wire to short "1a and "2a," the spots where the legs of the keyswitch go. Then test continuity between 1 and 2, 1 and 3, 1 and 4, 2 and 3, 2 and 4, and 3 and 4 (set your meter up to accommodate the diode direction for anything involving #4). Wherever you find the loss of continuity, handwire a jumper or bridge, including a new diode if necessary (though that seems unlikely). Well, don't jump 1 to anything else based solely on what I have here, LOL. That would be bad for other reasons.
I had lifted the "#2" pad on my keyboard, so I bridged from 2 to 3, and that worked okay for a while. When it didn't work over the long haul, I tried to rework my solder job on 2 and that also worked for a bit. That stopped and I handwired a diode between 2 and 4. That worked for even longer (not necessarily for the reasons I thought), but eventually failed as well. I think the torn pad affected traces nearby, or all my efforts messed up the socket, or
something, and eventually whatever I'd fixed came loose. Instead of beating my head against the wall and scraping , I used the whole board as practice for handwiring a large matrix. Lost my LEDs, and indicators, pending some more delicate work on my "new" circuitry, but it works again. The nuclear option, I guess. :-)
What I'm not sure about is #4 goes next. On my handwires, it would go to equivalent spots on the keys on either side, but there are no guarantees. Might be worth trying if the keyboard is otherwise useless to you and the other spots don't help. There's a real possibility that someone more knowledgeable than me will chime in though.
