What happens when you attempt to boot into Internet Recovery Mode? At what point does it fail? And do you get an error code?
If you never previously modified the Startup Security Utility settings to allow booting from USB, then it is impossible to do so now if you cannot boot into Recovery Mode or Internet Recovery Mode. In that case, your only other options are to try Internet Recovery Mode from another physical location with a good Internet connection, or you will need to try to perform a firmware "Restore" which resets the T2 chip, firmware, and will require reinstalling macOS from Internet Recovery Mode. The "Restore" is meant to address issues when users have issues reinstalling macOS. Unfortunately this "Restore" process requires access to another Mac running macOS 12.4+.
Revive or restore an Intel-based Mac using Apple Configurator - Apple Support
If none of this works, then you will need to have Apple or an Apple Authorized Service provide assist you and examine the laptop for possible hardware issues preventing reinstallation of macOS.
Edit: You can try a PRAM Reset (hold the reset for two chimes if possible). You can also try an SMC Reset (read the instructions carefully since the process is different for 2018+ models).
Also connecting the computer directly to the router using an Ethernet Cable and an USB-C to Gigabit Ethernet Adapter may be better since it will provide a faster more reliable network connection which also bypasses hard to troubleshoot WiFi issues.