Ventura docs for M2 Macs in this comment: https://gist.github.com/henrik242/65d26a7deca30bdb9828e183809690bd?permalink_comment_id=4555340#gistcomment-4555340
Old Monterey docs in this old revision: https://gist.github.com/henrik242/65d26a7deca30bdb9828e183809690bd/32c410e3a1de73539c76fa13ea5486569c4e0c5d
Solution for Sonoma: https://gist.github.com/sghiassy/a3927405cf4ffe81242f4ecb01c382ac
I don’t recall recovery mode asking for a password unless it was an encrypted disk.
su/sudo is not needed in recovery mode because you run as root (Adminstrator) by default.
It depends on what the issues is and what your goal is (what are you trying to accomplish?). If you are trying to erase everything, then apple’s official instructions are good to follow. Assuming you are here because of MDM, then you follow the instructions with no internet setup or blocking hosts via dns.