I just thought I’d mention this since it actually worked! (after some thinking.)
After an early Oct vacation the 2018 mac mini in my recording studio would not boot. I call that one Mini 2. It is running OS 10.13 . I decided to use the matching Mini (Mini 3) from the broadcast studio for recording and get a new mini for broadcast. (Recording uses old peripherals not compatible with newer OSs.)
I decided a clean OS install might be a good idea on mini 3 but could not figure out how to do it. So I decided to use the Recovery process only to find when the process got to the part where it tries to load the recovery page from Apple, that apple does not maintain the 10.13 recovery page anymore. (yes, their website says it is available but it is not) Now I had two bricked computers.
I finally bought a TB Hard Drive and made a clone of my 2014 Macbook Air also running 10.13. I booted mini 3 off the clone and it worked despite the hardware differences. It is also still working to date and I have already recorded several movies and hours of nature documentaries. Mini 2 appears to be dead.
The new mini (not the latest version) and OS Sonoma work very well in the broadcast studio BTW. Stable and easy to share to.
Another option would be to directly download a 10.13 installer image from Apple’s macOS download page.
Assuming you can download it (it’s an app store link, so I don’t know if incompatible Macs can download it, but your 10.13 laptop should be able to), you can then make a bootable installer from it, following the instructions on Apple’s support page.
From there, you should be able to boot the installer (follow the directions on the Apple support page for making the installer) and use it to install a clean image onto the non-booting Mac, assuming, of course, that the non-booting isn’t due to a hardware failure.
I have got a lot of problems lately with downloading old OS from apple servers, so it does not come as a surprise that you concluded it was not there anymore. You can still download 10.13. I just did.
I’d forgotten about actually downloading the OS. Recovery App failed during it’s own attempt to load their recovery page. I also tried to load the page from the Apple web site using their link but that failed too. I think Apple is just a little too bloated and concentrated on New stuff, where the profit is, too get it all correct anymore. Oh well.