Double coverage and HSA?

(I also posted in r/healthcare, hope that’s okay!)

Lovely people of reddit! Send help, I’m so confused.

I just got a new job. My primary health insurance will continue to be through my partner’s work plan, which is just a traditional healthcare plan (no high deductible, no HSA). It’s also probably worth noting that his company has truly EXCELLENT coverage and covers both of us at no cost to us, except $10 copays.

Enrolling in a secondary plan at my job has me confused though. We have two choices that don’t require me to contribute any money myself, so I’m picking between those two. One is normal health insurance similar to what my partner’s company offers, just not as good. The second option is a high deductible plan with an HSA option.

So normally I would think to just pick the first one because I know I can’t contribute my own money to an HSA unless my primary insurance is a high deductible plan. BUT I don’t have to contribute any money to the HSA for my employer to contribute $600/year. So if I choose the high deductible option with $600/year of exclusively employer-contributed HSA, can I use that $600 for copays and tampons and stuff? Or is this a tax no-no?

If I pick the non-HSA option, would having slightly crappier secondary insurance do anything to cover copays and stuff, or not?

Eeeeeeeee thanks for any insight!