How to clean up a Linux system to free up disk space?

What are some generic ways to free up lots of storage space without deleting personal files? I'm doing a distro upgrade (Debian11->12) and it needs lots of disk space on the root partition / which doesn't have a large size and I'd like to keep all user files on that partition with few exceptions if needed. A prior upgrade failed in the middle of it because of the error No space left on device and required more disk space than what was displayed when running for example sudo apt-get full-upgrade. Running step-wise distro upgrades that each require less disk space is not yet possible. Generic ways would be deleting caches and old logs rather than moving or deleting user files such as media files. Please include explanations what these things delete.