Obviously no separate partition for /home so my assumption fails.
There is a very precious and convenient tool to help finding ( and removing ) heavy folders or files :
ncdu
It’s a semi-graphical application that runs inside terminal and which you control using ←↑→↓ and some other keys. See https://computingforgeeks.com/ncdu-analyze-disk-usage-in-linux-with-ncdu/ or 10 Cool Command Line Apps for Ubuntu - OMG! Ubuntu! ( 8th § )
Did you try the « common » cleaning operations ?
# being up to date and without un-necessary cache or achive regarding apt
sudo apt update ; sudo apt full-upgrade ; sudo apt autoremove --purge
sudo apt autoclean ; sudo apt clean
# if you make use of snap applications
snap list --all
snap list --all | awk '/désactivé|disabled/{print $1, $3}' | while read snapname revision; do sudo snap remove "$snapname" --revision="$revision"; done
# here « désactivé » is the french word for « disabled », you should adjust to your language from what you find in the first list.
# residual installation of packages
dpkg -l | grep ^rc
sudo dpkg -P $(dpkg -l | awk '/^rc/{print $2}')
# or
dpkg -l | grep ^rc | cut -d' ' -f3 | xargs sudo dpkg -P
# cache for pictures thumbnails
find ~/.cache/thumbnails -type f -atime +7 -delete
# here the +7 means files older than 7 days will get deleted.
There may be some other tricks regarding logs and journal.