Question: How does learning about the political situation in Palestine during the first century help in understanding the New Testament?

That study will give context to post Roman rule in the area (called Palestine later)!

Also, it gives some context for the myriad of conflicting opinions regarding that periods’ many conflicting interpretations, which will leave the student with decisions to make, regarding what is decided to be believed!

IMO opinion, the student will have to decide whether to trust human comment, or Divine comment (the Bible), with comparisons to historians (such as Josephus)!

The large bulk of human comment derides the accounts in the Bible, as is to be expected, as the bulk of the population does not acknowledge the Bible’s accounts; see 2Timothy 3:16–17!

When a decision is made in the positive for Divine Writ, it is necessary to know which documents to study, which to some extent is helped with translations referred to in this Link: BIBLE Translations.