No. Any combination is possible. The server has its own set of private keys, that are in no way related your private keys.
I'm authenticating on a server using a pair of public and private 4096 bit Rsa keys, but once the connection is established, clicking on the yellow padlock, under "Server host key fingerprints" appears "Alghoritm: ssh-rsa 2048".
I have assumed that the asymmetric encryption with 4096 bit keys occurs only for the exchange of a symmetric key and then the entire session occurs with a 2048 bit encrypted connection: is my assumption correct or is there another explanation ?