When I try using the https://<IP_ADDRESS_OF_YOUR_PI_HOLE>/admin/ I get search results to access my router login.

Something is very wrong if you're getting search results, maybe try a different browser?

Checked downforeveryoneorjustme.com and it looks like pi.hole is down.

The PiHole website is https://pi-hole.net/ is that what you meant to check?

You can't check local private domains like pi.hole using a public service.

Try http rather than https

Aside from trying to reboot the pi-hole, you can also try plugging a monitor, and keyboard and mouse directly. You'll get a better answer. Just waiting is not usually helpful.

downforeveryoneorjustme.com would not help as your pihole is a local service accessible only within your network.

You are going to get a lot better advice posting on the pihole forum discourse.pi-hole.net

I'd check its IP in the router then try and access it via http, not https.

But my version in still 5.something and v6 could bring https, I have yet to update my LXCs

Is that something you control? Because pi.hole is not a registered domain name. (And I wouldn't trust a random person's pihole anyway.)

Assuming it's your local pihole and you have DNS set up, I would check that configuration start to finish.

Did you update from 5 to 6? That introduced a bunch of fuckery