How security is maintained when you run commands via ssh?

Good day colleagues!
We are interested in the following issue.

1) the Generated ssh key
2) Casting it on your target machine (server in my case)
3) Connect to the server
ssh user@host - all good here, no questions
4) run the command
user@host # ls-la

When connecting to the target machine (item 3) validation logic is key to me clear, to access the server we got.

When we try to run the command (principle no matter what, let it be ls-la) (para 4)
are there any additional checks on the server from the security point of view?

Have this crazy theory that every time you run the command the function checks the keys, I think most likely it is not.
Can someone tell me which algorithm you run the command on the remote machine? (Assuming that we are already connected to the server).

It will be enough source where it can be read

Thank you all.