You are quite right. Yet there is a report on this thread to the effect that (partial?) Immunity was granted in exchange for access to her laptop? Why would immunity be granted to obtain something that was readily obtainable through a subpoena or search warrant?
Limited immunity probably would give her the best of both worlds, protection against prosecution and protection against being required to waive her Fifth Amendment rights not to testify because conceivably her testimony might incriminate her for some act that was not covered by the immunity agreement.
Without knowing more, I agree with the second half of your reply.
There were reports, or rumors, that the FBI had begun an investigation of the Clintons' foundations and that would carry things forward and involve most of the same people. Not sure if those reports were ever verified or disproved.