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as a non US-person who recently wanted to look at some cases: is there a free way to do this? Or do you have to sign up to the weird ePACER?

Every document at SCOTUS level is freely available, although you have to know the docket number to get all of the briefs correctly. SCOTUSblog in practice is a more accessible interface to the docket, since you can easily look up by case name: https://www.scotusblog.com/case-files/terms/ot2023/, e.g., the full docket for the case in this article is here: https://www.scotusblog.com/case-files/cases/harrington-v-pur...

If you want to deal with non-SCOTUS federal cases, your choices are to use PACER or to use RECAP (https://www.courtlistener.com/recap/), where the documents may be available. E.g., the appeals court docket for this case is at https://www.courtlistener.com/docket/67448481/in-re-purdue-p..., note that many documents aren't available because no one made it free via RECAP.

If you want to deal with state courts... good luck! Every state has a different system with different level of pains to track down.

You do not have to sign up for anything. SCOTUS opinions are freely-accessible public record.[0]