It would definitively be interesting, if you can build a v0.11 version that works, since your dmesg is quite clearly showing that even the Linux OS is having hard time with the board.
Just for the fun of it, a klipper.bin compiled by me. Unfortunately, due to different underlying Linux OS you cannot compare the md5sum:
v0.12.0-125-gbfb71bc2 (22.6 KB)
If nothing else helps, I would try this as well. Maybe a messed bootloader. In any case, all my boards get katapult as it is way more convenient to update. See CanBoot: Flash BTT SKR 1.3 / 1.4 / 1.4 Turbo