I would guess the reason Wikipedia doesn't cover the bank is that it's not notable enough for an article (four branches). As for the bank previously being a branch of another entity, in the US, "First National Bank" is a generic phrase used by many unrelated standalone or small networks of banks. There are indeed national banks here (e.g., Bank of America or Wells Fargo), but they're commercial in nature and not operated by any level of government.

This bank is notable enough for Wikidata – here’s a new item for it. It was always an independent bank, not a branch of another bank. “State-chartered” means they chose to register with a state regulator instead of the federal government. (Unlike in other countries, “national bank” only means a federally regulated bank, whether commercial or retail, almost never a government agency.)

NSI has many state-chartered banks, but coverage is very incomplete, especially for small banks with only a handful of branches.