if you are using server component and fetch the data from external backend, it will be sent back to the server first and not the client. So yes. This will slow the webpage more than using a client webpage. But you can use streaming and caching so that users can receive the website instantly before your backend finished returning data to the nextjs project.

Is it better to just use a client component?

Yes. It depends if you want the benefit of server rendered component or not. Some people finds it easy to implement fullstack app with server component and client components, some people just go full SPA

does the client component get entirely rendered in user's browser or the server renders some part of it already before sending the response?

the latter