An extreme (but data cleansing thorough option) would be to export all (of your user folder) to an external drive, wipe and fresh install the OS to the internal drive. That should free up almost
ALL of your space on the internal. Then, import only stuff you absolutely want on that internal considering size (check size on external) and then import suitable stuff. This is a much more onerous, one-time project to re"start from scratch" but it will blow out everything and then you can carefully consider exactly what you want to reinstall vs. stuff perhaps no longer important to you.
Start by reinstalling applications you use and then see how much space all important applications installed eat up. Don't install applications you no longer use. This alone can make a good-sized difference on the drive. Over time, a lot of "one off" applications can control a chunk of space with little chance of ever getting used again.
Non-application priority might be some stuff that likes to "live" on the internal like music (rips) and photos library... though if either or both of those eat up most of the space, they don't absolutely have to be on the internal.
- Movies folder could definitely live on the external going forward. If this is currently sizable- as is common- shifting it to external alone may free up a great deal of space.
- Empty Downloads.
- Documents folder could live on external.
- Clear Desktop.
- Public could be empty unless you need something permanently shared with anyone else on your network.
This would be equivalent of "clean install" and would also get rid of accumulated clutter in many hidden places. While that clutter probably doesn't eat up a lot of space, it can take up some.
As you re-install, keep track of how much space is used. When you get to about 125GB, I'd shift most of my thinking to storing everything else on the external (basically keeping about 50% free). As you move forward, macOS and/or software upgrades will eventually turn 50% into 60% and so on but if you target about 50% now, you'll probably be good for remaining life of that Mac.
If Desktop really is controlling 150GB, the easy option is to move everything on Desktop to an external and then don't reload the Desktop: keep it clean. No consequence to storing stuff currently accumulated on Desktop on external.
Again, the "clean install" option is not as easy as looking through everything and deleting or moving files to the external. This is equivalent to "starting over" like it's a new Mac. But this will really cut the accumulated files and when you consider what must go back on it again, your scrutiny should lead to a much less loaded internal drive.
One more thing: several places make a same-size (as Mini) docks with built in storage. You might want to get one of those and a good amount of storage as a permanently-connected drive...
Unlike the typical portable enclosure, there should be little to disconnect that drive and that thing can easily come forward to your next Mac Mini (or Studio) purchase too.
Lastly: if not already, get Time Machine going and back up both the new internal and that external drive, ideally to 2+ drives with at least 1 of those stored offsite. Rotate the on-site and off-site drives regularly so that you have a pretty recent backup of all of your files at the offsite location. I use a bank safe deposit box for the offsite storage and swap mine monthly. Worst case scenario is I lose the last 29 days of new data.