Try it although it might very well be limited to Monterey and up.
What does the Terminal "softwareupdate --list-full-installers" say about your download options? For my Mac mini 2018 that supports Mojave and up, it lists:
softwareupdate --list-full-installers
Finding available software
Software Update found the following full installers:
* Title: macOS Monterey, Version: 12.1, Size: 12157035487K
* Title: macOS Monterey, Version: 12.0.1, Size: 12128428704K
* Title: macOS Big Sur, Version: 11.6.2, Size: 12433351292K
* Title: macOS Big Sur, Version: 11.6.1, Size: 12428472512K
* Title: macOS Big Sur, Version: 11.6, Size: 12428553042K
* Title: macOS Big Sur, Version: 11.5.2, Size: 12440916552K
* Title: macOS Catalina, Version: 10.15.7, Size: 8248985973K
* Title: macOS Catalina, Version: 10.15.7, Size: 8248854894K
* Title: macOS Catalina, Version: 10.15.6, Size: 8248781171K
* Title: macOS Mojave, Version: 10.14.6, Size: 6038419486K
Then, if possible, download Monterey, Big Sur and Catalina full installer, make a bootable USB flash installer and try to boot them (after enabling external boot in the Recovery mode as you apparently already have done).
https://support.apple.com/en-us/HT210190
https://support.apple.com/en-us/HT201372