are there bluetooth keyboards and mice that will work with 2018 MacMini

Most if not all BT mice and keyboards should work.

Have you set the old ones to pairing mode as explained in their own instructions?

Do they use a dongle? Many older dongle requiring keyboards and mice are RF based rather than Bluetooth so they won't work without their own dongle.

If they are true Bluetooth, make sure they aren't currently paired to anything else, and set them to pairing mode as per their own instructions.

I'm using an older BT Apple keyboard with my mini so your problem may not be compatibility but rather interference. The location of the BT antenna on the mini makes it vulnerable to interference from badly shielded USB cables, external drives, and hubs. I discovered the problem a few years back when I purchased a USB 3 hub for my iMac. I wound up moving the hub to the far left of my keyboard and mouse which mostly solved it. A couple days later I found a source for shielded USB cables and that totally solved it.

So you might first try turning off all the peripherals plugged into the computer and move the computer to the left side of the display. If your keyboard and mouse pair and work try turning on USB devices one by one. If you lose connection you'll know which is to blame. Simply moving and/or replacing the cable may solve it.

Tons of them, sure. I use a Logitech K750 solar wireless keyboard and a Logitech MX ERGO wireless trackball with my late 2018 Mac mini. I do use the Logitech universal connection dongle though, and not MacOS BT for the connection to avoid any possibility of BT interference from other nearby peripherals. But I did connect it via a regular BT pairing before and it worked just fine.

What model of older device are you using? I’m surprised that an older device wouldn’t work either.

In addition to the other excellent comments, I use the Logitech MX Master 2S mouse with my 2018 Mac mini. As Phil0124 has mentioned it's an RF-type mouse and requires a small USB dongle to be connected to your mini to work.

FWIW, I got this mouse and associated Logitech K780 Multi-Device keyboard because I need to support both this mini and a Windows 10 desktop. Switching between them is very easy and because it works with RF, it doesn't interfere with my BT headset.