Comment by fragmede

Check for yourself with

    ssh -v -i /dev/null terminal.shop

vs

    ssh -v terminal.shop

What you're looking for is that there is no line that says something like

    debug1: Offering public key: /Users/fragmede/.ssh/id_rsa RSA SHA256:xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

Upon further testing, the full command you want is:

    ssh -a -i /dev/null -o IdentityAgent=/dev/null terminal.shop

to forcibly disable a local identity agent from offering up its identities as well, and not just agent forwarding.

Upon further testing,

    ssh -o IdentitiesOnly=yes terminal.shop

still offers up my public key on my system (macOS, OpenSSH_9.6p1, LibreSSL 3.3.6), contrary to what StackOverflow and the Internet seems to think. Tested by hitting whoami.filippo.io, linked in child comment.