2018 Mac Mini (Intel) shut down on it's own

Your MM is suffering from Kernel Panics which can either be caused by failing hardware such as a failing HD or third party external peripherals that are failing. They can also be caused by software. I recommend starting to troubleshoot by doing the following:

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None of the usual software suspects show up, however your system is 8 years old which means there is a good chance it has some pretty outdated third party apps installed. I would check is to see that ALL of your third party apps are up-to-date. This is kind of tedious and is also not a guarantee this will fix the issue. To update them some will have a built in utility that tells you they are out-of-date and needed to be updated so you need to startup the apps, check within the apps for such a utility (normally listed in the Menu under the apps name) and if they don't have such a utility you have to go to the developers web site to check for updates.

However, before going to that exercise the first thing I'd recommend doing is downloading DriveDX and running a report on your internal HD. Your system has a Fusion Drive (combination of a small SSD and a traditional spinning HD), I suspect the HD aspect may be failing!! So run the report and look under the HD section. IF ANY if the HD shows errors that simply confirms my hunch. While you are at it you should also check any external drives too as they can cause KP's too if they are failing.

So that gives you enough to get started on. My suggestion IF my failing internal HD hunch is correct would be to simply get yourself a new M4 based MM. All of these will far out perform your current machine and be a HUGE upgrade for you.