You answered your own question by later using apt dist-upgrade rather than apt upgrade
You would see definite errors if the upgrader had failed again. If everything cleared after your second attempt, I would think it likely you are fine.
Yes. If you are not seeing the home directory filled with clutter from Downloads, Music, configuration files or other media, then most likely a lack of space will take place in Root - specifically, filling up /var/log files. They can really gobble up space.
What you can do - and also can script is a journalctl --vacuum command to occasionally clean out logs. You can set this up either by size or by time frame, so I recommend you determine your needs, first.
I will give two examples:
sudo journalctl --vacuum-time=7d
sudo journalctl --vacuum-size=100M
The first allows the system to retain logs only younger than 7 days. The second, cleans out old logs to keep the maximum size of the directory to be less than 100 megabytes.
You can set these as a script along with sudo apt clean && sudo apt autoremove to run upon every boot,.