Auto-lock can be disabled by installed profiles, so it cannot be changed from Immediately.
Usually Microsoft Exchange Email accounts(corporate or school based) will do this when added to a device if they have security profiles attached.
Check Settings ➜ General ➜ VPN & Device Management, and see if there's a Profile installed there.
It's unlikely the mouse would add such a profile, since it cannot run software over bluetooth or even USB-C.
The other option, is that you have Low Power mode active. This will disable the Lock-Out option, as it forces the screen to turn off and lock quicker to preserve battery.
You can open the Control Center, and look for the Yellow Battery icon, and tap it if it's turned on, to turn it off.
I guess the real question is: How did you install this mouse? Beyond plugging it in, or simply paring it over bluetooth, there should not be anything else you can or need to do.