What you're missing is that, to create a signature, you need to know the private key corresponding to the public key; it's an asymmetric algorithm.

> Client takes its own public key and the server's public key and creates this signature.

According to https://www.rfc-editor.org/rfc/rfc4252#section-7 client takes its own public key, the "session identifier", and a few other things, and creates this signature (using the private key corresponding to that public key). According to https://www.rfc-editor.org/rfc/rfc4253#section-7.2 that "session identifier" is a byproduct of the key exchange.

> MITM can take its public key and the client's public key and send the resulting signature to the server instead of forwarding what it received from the client.

That's not possible, since the MITM doesn't know the client's private key (and using a different public key will be rejected by the server).

> Do pretty much the same exact thing: MITM PK + Server's PK -> Client. Now client has a signature as well. The signatures that client and server have are different but that is OK as long as MITM can see and change all communication.

You're confusing the Diffie-Hellman Key Exchange with the Public Key Authentication Method. When you MITM the key exchange, the shared secrets the client and server have are different (one side has a secret derived from the client and MITM keys, the other side has a secret derived from the MITM and server keys), but that works as long as the MITM can see and change all communication (basically, decrypting it and encrypting it again).

But since the secrets are different, the session identifier is also different. The MITM can't forward the signature from the client since the server will fail to verify it due to the mismatch in the session identifier; the MiTM can't create a new signature with the client public key since it doesn't have the corresponding private key; and the MITM can't create a valid signature with its own public key (and the corresponding private key) since that key won't be in the authorized keys list for that user account in the server.

Stop MitM on the first SSH connection, on any VPS or cloud provider