An MFP uses installed software, and the software does not need anything else when it works. But recently some types of software need a server to work.

I'd call this software "Server-supported software", but does this make sense?
(It's okay if it is roughly understandable.)
Try server-dependent software.
SupercatIt's okay if it is roughly understandable.
To me, it sounds like the software can be used in that server. Is that what you mean?
Students: We have free audio pronunciation exercises.
Then the OP is wrong. The software works with/connects to the server when it operates. How about "Server-linkage software"?
Supercat How about "Server-linkage software"?
That sounds better to me—but I am not terribly computer-wise, so wait for a 2nd opinion.
Students: Are you brave enough to let our tutors analyse your pronunciation?
Lol, I don't think you're so! Thank you.
 teechr's reply was promoted to an answer.