I think you may have misunderstood your issue. 16 GB is more than is needed on / for a typical desktop Ubuntu installation. For example, here is a partial output of df -h on my Ubuntu 22.04 system- this is a server but it has a full desktop environment installed. I actually originally put 20.04 on it when that was current so it has accumulated some cruft. I also remove snaps:

The thing you're most likely running into is that whilst everyone quickly realises the advantages of putting /home on a separate partition, it's not so obvious that /var should be on a separate partition as well. This is because /var is where all the logs and caches are stored, and if you have a runaway process that fills up /var/log, it can cause the system to crash. Experienced Linux users will have encountered situations where /var was not on a separate partition and their box broke because of logs not being cycled...

I realise that you may be saying that you have 16GB total for 2 x installations. That is going it a bit but should be possible with some thought and care. Good luck!