In the error log there is a line unix_chkpwd[842]: could not obtain user info (gdm) I’m not sure what this means and if there is a issue with the gdm user, that could maybe explain gdm not starting. What is the status of the gdm service?
How have you reinstalled gdm? there is gdm-plymouth & gdm available.
From a announcement from stable update thread: on gdm and gdm-plymouth:
Log into your system via tty and depending on your use of Plymouth or bootsplash-systemd choose a option from this post