Hello,
To set your macOS virtual machine in bridge mode, kindly shut down the macOS 13 virtual machine and open Terminal on your Mac and execute the command below:
prlctl set "<vm_name>" --device-set <network_adapter_id> --type <bridged/shared>
e.g.:
prlctl set "macOS 13" --device-set net0 --type bridged
Kindly refer to this article for more information regarding Configuring macOS virtual machines running on a Mac computer with Apple M-series chip:
https://kb.parallels.com/en/128842 .
Thank you.