Photos app capacity on Mac Mini

Yes, a Mac mini will handle 7k images and videos, though I wonder why that few items use 2.3 TB of space. Are you storing full length Hollywood movies?

Equally the Mini will handle twice that and even 10 times 7 thousand items easily.

Theoretically the Photos app is unlimited in the amount of material it will manage. What might limit you is storage - that is actual disk space. But even that's not a real issue as you can store the library on an external disk formatted Mac OS X Extended, Journaled or apfs. (Note: it cannot go on a NAS)

Certainly as libraries get large they can have performance hits. At what point that cuts in will depend on factors like the available disk space on the Mac, the amount of Ram and the length of a piece of strong. But I would expect that before you hit that kind of barrier you'd be having 150k plus images anyway. And you can also have multiple libraries.

"Length of a piece of string" is usually used to refer to some arbitrary measurement.

I use multiple Libraries, and their use is, more or less, defined-- so I don't have to search multiple libraries at once. There are overlaps, which I don't mind. I have my wife's family pictures and my own family pictures in separate libraries, because I don't really want to see all those all the time. In any case, while Photos can't, the trusted 3rd party app PowerPhotos ($30,) which we use to deal with multiple libraries, will search through them all libraries at once. I have a small subset of my pictures in a Favorites Library which I connect to iCloud to synchronize on my iPhone and iPad. I can keep this Library on my internal drive.

We've found that an external drive doesn't do so well at accessing location lookups, and we hope that will be fixed. (Who knows?) Connecting an external drive Library to iCloud is problematic for a portable device, but it should be no problem with one connected to a desktop Mac full time.

What does "length of a piece of strong" mean?

It means that I can't proff reed. :) What I mean to say there is that it's impossible to predict at what point the performance hit will cut in to a noticeable (and irritating) extent, there are just too many variables.

With USC C drives there really is no performance hit using external storage. All of my images are stored on external drives - which incidentally are a lot less expensive than internal storage.

I was also going to recommend PowerPhotos.

I guess I would say the following: No need to over think this. This Mini may be on the lower end of the Mac computers but it is far more powerful than almost any Mac from 5 years ago.