You are mixing two concepts here, perhaps unintentionally. The supreme court has a standards document against which it evaluates the laws (the constitution, whether it is state (SCOC) or country (SCOTUS)). I have not read a decision where they evaluate "what the legislature 'meant'" when they make their rulings, although they do sometimes comment on that.

The Supreme Court absolutely interprets the meaning of federal law passed by the legislature. Whether they do it by appeal to authorial intent or something else is a matter of jurisprudential philosophy.

For an example of talking about what the legislators intended, see King v. Burwell: https://en.wikipedia.org/wiki/King_v._Burwell

Our two main political parties constantly fight to appoint their preferred candidate to the Supreme Court. If the Supreme Court were just following some apolitical procedure of interpretation, none of that would be necessary.

"some apolitical procedure of interpretation"

I'm down. But who gets to decide what's an apolitical procedure of interpretation? And what does that even look like?