where to find older MacOS for download

My Wife's Mac mini (Late 2014). I think it had 10.11 since new.

It was time to update the OS - finally - So I started the process. After a couple hours, I had the new operating system. It now has Monterey. OS 12.1.

What the heck?

The first problem is that it runs like molasses in winter. 4GB RAM and a 500 Hard disc drive.

I'm really upset I couldn't even get her Mac mail to work (Google server). I can only get it through web-mail.

I didn't want that OS. I was just hoping to get something newer than 10.11. Perhaps Mojave. High Sierra.

Instead I ended up with Montezuma's revenge.

Luckily, I backed up the important stuff.

I wiped the drive hoping that I could just install something newer than 10.11 via USB. I've done it before on other machines in my home. Should be no problem.

Big problem. I can't download anything other than Monterey.

Using other Macs, I've gone to the "support" page and follow the trail to the OS I want to try - takes me to the App Store, no download or get button. I can see the preview page for a bunch of OS's, but I can't download anything on another machine - to make a bootable USB device - and then wipe and start fresh.

Tried every conceivable method to get a proper working copy of the OS. ANY OS that is compatible with this lowly mini. No luck. I even checked out non-Apple sites, but thought the better of it.

I'm not interested in getting more memory and an SSD drive to help with performance (it is such a dog).

If anybody knows something I don't, I would love to hear it.

I saw another post that said I could install the originally installed OS on the machine by doing a restore from the internet, but then what - if I can't bump the machine up to a newer OS (not Monterey!!), then I'm still stuck.

Thanks Apple - "Look what you've done to my boy!"