How long before you're considered a resident of a state?

Every state requirement is different.

Back in Va., when I was a LEO, the State required shipyard workers
who worked in Norfolk but had residences in N.C. to have a Va.
Operator License. Why? Because they had a full-time job in Va.
Per State Code they were required to have a Va. O/L.

I understated that it was finally changed after 40 years or so.

There is no blanket statement that covers all states.