What should be the order of a SaaS-Product launch: HN/PH/Reddit/Twitter?

The order doesn't matter, but you prob want to be available for comments/replies in case the launch goes particularly well, so do them 1 at a time.

Twitter feels pretty irrelevant to me, unless you have a massive amount of followers. Don't use Twitter to promote PH or the others, because you'll get banned or penalized.

I'd generally launch first on the platform where you have more experience, if any. Unless you want/have to test your launch, in which case choose the 2nd and use any learnings for the 1st.

It really doesn't matter - your launch should primarily be to your audience. The platforms are a nice bonus, but shouldn't be the core focus of your launch.