I've heard it referred to as a ''no-questions-asked 30 days refund'' (but it's not exactly phrased that way in the announcement post). Is that accurate?

For technical issues: https://support.gog.com/hc/en-us/articles/115000487189-GOG-COM-Money-Back-Guarantee-Policy?product=galaxy
General money back guarantee: https://support.gog.com/hc/en-us/articles/360006129837-Update-to-our-voluntary-Refund-Policy?product=galaxy

Well, the pages contradict each other on some points, but if the more recent one supersedes everything in the old one, then it sounds like it's optional to ask for tech support and you can just skip straight to getting your refund.

You can, yes. Although they seem to review the request manually, which means that (a) they can still theoretically deny the refund if they feel that you're exploiting the system; and (b) it might take a while for you to get the refund, when Support is swamped with other requests (during the last sale, they said it could take up to 4 weeks before support tickets - including requests for refunds - were answered).