M1 Macs cannot use USB tethering to provide a network while in Recovery Mode. This is the same as your experience on an Intel Mac.
The RecoveryrecoveryOS UI only presents options for connecting to WiFi, or wired Ethernet networks (with the addition of a Thunderbolt to Ethernet adaptor for MacBooks). The USB tethering functionality is contained in the Network Preferences pane under a normal boot of macOS. That has the option to manage the full gamut of network hardware, such as WiFi, USB, or Thunderbolt Bridges.