While I understand the utility of a USB installer, it should be mentioned that macOS Internet recovery has been around since Lion. You can choose to install latest ...
If you have a spare hard drive lying around, you could use the existing recovery partition to install the OS on to that, even if just temporarily. If you have a friend with a Mac, he could download ...
macOS Monterey version 12 is a stable, lightweight upgrade that works great on older Macs, and you can use the direct DMG or ISO links to download, install, upgrade, or downgrade your system easily.