UPS not showing in Energy Saver?

You are not doing anything wrong. As far as that Mac is concerned, the UPS is simply not present.

You don't need to install any software either. It uses Java which is outdated and just a bad idea anyway. macOS already includes software to recognize the presence of a UPS so you need nothing else. Throw the CD in the trash. Just plug in the UPS's USB cable, and a new UPS tab should appear in Energy Saver.

Since the device does not appear in the USB device tree, nothing is going to happen. Either the USB cable is broken, or the USB port on either the Mini or the UPS is not working, or some combination of those possibilities. Unless you have reason to believe your Mac Mini's USB port is not working, the UPS is probably defective.

I think the best option would be to buy a UPS that works without a requirement for any additional software. The requirement for Java is a very bad idea alone.

If you can find one for sale in Bulgaria, I know APC models work.

Add-on software might not work, but even if it does, it might stop working with the very next macOS upgrade or update.

Using the MacBook Pro might not be a valid test. Since a portable Mac always has power and will sleep or initiate its own orderly shutdown in the event of a low battery condition, using a UPS makes no sense with one. It's certainly not something Apple would consider essential.

Edit: I take that back. I plugged an APC UPS into a MacBook Air, and it appears in the Energy Saver Preferences as well as in the USB device tree.

So that returns me to the same suspicions: an inoperative USB port on that UPS.

I understand your concerns. Some of my locations have absolutely lousy power. I use UPSs and diesel generators because I can't have the Macs shut down.

I thought all UPSs worked, until reading your story. I am not familiar with the njoy 850L UPS.

In addition to APC, Cyberpower is another model worthy of consideration.

I have a 2012 Mini and use a Cyberpower UPS. No software required. Just connect USB cord and Mini recognizes it, no problem. Get power loses all the time and this unit has work flawlessly

If your power is that bad I don't blame you.

I lost plenty of equipment due to lightning. Unfortunately the UPS didn't protect it. Fortunately APC made good on their equipment protection warranty. I don't know if they offer it any more.

I understand your difficulties. A UPS is the obvious solution, along with an automatic gas or diesel generator for prolonged periods. All my Macs need to be up and running all the time.

You can also set Energy Saver to automatically restart the Mini after power is restored. If that does not work or if it becomes difficult to start after power has been removed for some time, the cause is almost certainly a depleted PRAM battery. That's easily replaced.

The power supply itself is robust, especially for consumer grade equipment, so it should be OK. I doubt any testing equipment is necessary.

... they all say that typically that battery is fine for about 10 years.

Yes it is, unless the Mini's power is disconnected for prolonged periods of time, or many shorter periods of time. Ten years is their shelf life. If they're actually needed they will not last that long.

In any event if you ever need to open the case for some other reason, they are too easy and inexpensive not to replace.

Now, I'm hoping that the UPS would solve the issue by automatically shutting down the mini even if I'm not around.

It should.