Yes, the server knows your public key. In fact, unless you have specified which public key to use (via command line option or ~/.ssh/config), the server receive

Yes, the server knows your public key. In fact, unless you have specified which public key to use (via command line option or ~/.ssh/config), the server receives all your public keys. This is identifying information - most people have at least 1 ssh public key in github, and github makes those completely public as well. Filippo Valsorda from Cloudflare built a demo of this - try running: ssh whoami.filippo.io and if you have any of your keys in github, it will identify you. If you want to avoid this you should configure ssh to only send a single specific key.