Following up on what I said in D10184:
Once I get an answer there, I'll decide on how to proceed for desktop, and submit some follow-up diffs to enable unused-promise for it as well.
I received a partial answer, and did some follow-up research myself. It looks like we can treat desktop like native and web, since it doesn't crash on unhandled promise rejections, unlike keyserver.
As such, this diff mostly prefix invocations with void, with one exception where I add an await instead in an async IIFE where the result is thrown away anyways.