I still would wait to mention the New Republic until the second paragraph. The Imperial Remnant is the prime antagonist, and The Mandalorian is the protagonist. They are who should be in the first and third paragraph, with other elements of the setting between. The New Republic is too anecdotal to the story, even with the whole season. I think you should, like story does, kinda brush off the New Republic as insignificant.
Exactly. We dont need to exain too much the situation in the Galaxy in the opening crawl.