Can "what" be a relative pronoun?

Unlike which (which has the antecedent "the entire population"), what does not have an external antecedent in that sentence.

Rather, this is a "fused relative" construction: "what feels like light years away from a hospital" functions like a noun phrase consisting of a nominal head followed by a relative clause: something that feels like light years away from a hospital. What is fairly commonly used in fused relative constructions in standard English, even though what is generally not used as a relative pronoun with an external antecedent.

The meaning of the sentence is therefore similar to the following (where just "light years away from a hospital" is used):

These specialty jobs are integral to the daily well-being of the entire population, which lives in near isolation, light years away from a hospital, a department store, and the internet.

Saying "what feels like light years away from a hospital" makes it clear that it isn't literally light years away.

A shorter sentence that would show the same usage would be "The entire population lives what feels like light years away from a hospital."