That's a us postal service zip code.
The US Postal Service still exists, in the age of Transporters?
In the UK, postcodes (our equivalent of zip codes) are used for navigation as well as just the post (I might enter B604BE into my sat nav if I wanted to visit that part of the Midlands). Very occasionally they get used colloquially (the Wimbledon tennis tournament is fairly often referred to as SW19 - its postcode).
Why would Bev call the US an "Old Nation State" if it was still a thing in the 24th century?.
Perhaps to indicate that she was referring to the "old nation state" rather than to the administrative area that any of her contemporaries would have understood by the phrase.
The "United States of America" is a purely artificial entity and as such makes no geographical sense: it excludes areas of land that are physically attached to it (Canada) and includes areas of land that are detached from it (Alaska or Hawaii). We know from TNG that the country has gained two states compared to 2022. We *don't* know where those states are: were two of the "non-state" parts of it "statified" (perhaps DC and Puerto Rico?); did two existing states split into four (Texas and California perhaps); perhaps adjacent territories got absorbed (one way of dealing with all those Mexican immigrants lol); or did two attached territories join up?
https://www.youtube.com/shorts/_S2r58B4RKA
The Union Jack is a composite of the Northern Irish Flag, the Scottish Flag, and English Flag.
If Northern Ireland Secedes, or if Scotland secedes, No Longer So Great Britain has to find a new Flag.
When first created, the Union Flag only represented the countries then in the Union: England and Scotland. AS such it had the English George Cross superimposed on the Scottish Andrew Saltire. The Irish Saltire was added 200 years later. Presumably, if England and Ireland were to gain their independence from Scotland

Just as post-monarchical countries like Germany and Greece still have members of their former royal families who claim titles I'm sure Trek Era Britain also has Windsors who claim ties to a King or Queen from centuries before.
I've read (admittedly fictional) stories where people claim to be "next in line" to the French throne, I 've read this enough times that I imagine there are real people who do so - even if without any expectation of receiving their "inheritance."
Absolutely, but with the EU each country still has a President or PM, plus (I'm guessing) local government leaders. I'd say that on a united Earth, "member countries" would at least have a representative, if not a President. Hopefully smaller government can work.
The entities that comprise the EU are independent states, they just recognise, generally, the EU as having a large degree of authority over them.
dJE