Download mac os from the app store to external USB
If you want to have a copy of the macOS installer on an external drive, it's fairly easy to download. This link (https://tidbits.com/2019/10/28/redownload-archived-macos-installers-to-address-expired-certificates/) contains links to several versions of macOS.
These installers are just applications, and how you download the installer varies depending on which version of the operating system you're trying to download. Recent versions require using the Mac App Store to download. It will show up in your Applications folder. After it's finished downloading, just drag it to your external drive.
Apple doesn't make finding these files easy; it wants everyone to use System Preferences to update or Recovery Mode to reinstall. I suspect that's because it's the best way to make sure you have the most recent version (security patches included).