A bootable macOS USB installer compatible with an Intel Mac should appear as an option on the Apple boot picker menu when you Option Boot an Intel Mac. Option Booting is when you hold the Shift key immediately after hearing the startup chime on an Intel Mac (best to use a wired keyboard when using special startup keys especially if you cannot activate the special startup modes). This is regardless of the security settings.
The security settings only come into affect on an Intel Mac once you select the external boot volume from the Apple boot picker menu when Option Booting. If the security settings don't allow for booting from USB on an Intel Mac, then instead of booting from USB drive, the process will launch Recovery Mode where you will be given a chance to configure the security settings to allow booting from USB.
You will not see the macOS USB installer as an option in the Startup Disk System Preferences/Settings app no matter what the security settings are configured.
No idea about whether the Security settings matter on Apple Silicon Macs when trying to see if an external boot drive is shown as an option in One True Recovery mode. I haven't tried booting an Apple Silicon Mac from any external media yet.
Please be very clear & specific where you are referencing not being able to see the macOS USB installer and the exact model Mac you have since that may be a very important item here as well. You can get the exact model of the Mac by clicking the Apple menu and selecting "About This Mac", or if you cannot boot macOS, then entering the system serial number here:
Check Your Service and Support Coverage - Apple Support
It would also help to know the version of macOS USB installer we are dealing with as well to make sure it is even compatible with your exact model Mac.
The common issues for not being able to boot from a macOS USB installer are:
- USB installer was not properly created using the Apple instructions
- The USB stick being used is not compatible or possibly is not good. Macs are very picky about the drives used for booting and the quality of USB sticks is extremely poor. Best to try using another USB stick especially from another brand.
- Make sure to connect the USB installer directly to the computer. Disconnect all other external devices in case one of them is causing a problem.
- Maybe the USB port on the Mac is not fully functional....try using another USB port especially on the other side of the laptop.
Just noticed you are not the OP and are running an M1 Apple Silicon Mac...disregard the information at the beginning about Intel Macs, the other items later in my post still apply to Apple Silicon Macs. You really should have started your own thread.