FP 3 : Updating to Android 13

There is no documented way to collect a log from eosinstaller so one is just guessing. You might check some other threads with that hastag for inspiration.

FP3 is now installed by script in the CLI manual install method and there is this tutorial [HOW-TO] Flash /e/-OS on Fairphone 3 using Debian based GNU/Linux. This might be a better bet than troublshooting the installer which seems not to work for all.