I had a similar problem today. I booted with a system configured with Guix at 275fcffc9b5f4deb516c510b26b07c13d6e47307 and everything worked fine. Then I reconfigured with Guix at commit 04b83678653fda3c66e600e88f54f5108290ec1c, removed a few dozen old generations and did a 'guix gc'. At the next reboot, gdm didn't work anymore. I rebooted and launched the previous system generation, but gdm still didn't work, which is strange. After some investigation, I found that gdm was failing because the kernel driver for the GPU was not loaded (the 'nouveau' driver in my case). I tried to load it by hand with 'insmod /run/booted-system/kernel/lib/modules/5.9.11/.../nouveau.ko.gz', and it failed with the error 'unknown symbol in module'. I'm not sure what was going on here... The only way I got everything to work again is by reconfiguring the system to compile and use the 5.9.12 kernel.