It usually depends on how big the road is that you're driving on. Most state borders are in very extremely rural areas, so sometimes there's not even a sign. On interstate highways it's always quite obvious, but little country roads might not have any signage at all.

• There's usually no obvious change in architecture, no; often the only architecture is farm buildings, and those are more or less consistent architecturally. And broadly speaking architecture is regional, rather than state-specific; the difference in architecture from northern Indiana to southern Indiana is far more pronounced than the difference in architecture from southern Indiana to northern Kentucky, for instance.

• As noted elsewhere, sometimes the infrastructure can be different (usually seen in road quality), but most states tend to number their county roads in different ways, so when you cross the border you'll often find that the number of the roads you're crossing tend to suddenly shift from "300W" to "2300E." The signage may also change very slightly, though if you're truly out in the middle of nowhere, there might not be any signage to change.

• Agriculture, like architecture, is usually much more defined by region than by state. All of the states around mine farm corn, wheat, and soybeans, just like mine does. Most also farm cows, though Kentucky notably has a lot more horses than any of its neighbors, so that can be a tell. But you don't get into a ton of ranching until you get further west, and then you see large changes across multiple states at a time.

• Store brands often do change, but again, since most crossings are in rural areas, there often aren't any stores around to notice the change right away. You'll roll out of a state with a lot of Meijer stores and into a state where Publix is the regional grocery store, but until you get into a town, there's no way to know.

• Culture is probably the thing you'll notice least. People who live in rural areas tend to think of themselves as American before any other identifier, so you'll find a lot of jingoism anywhere on both sides of any border. American flags, Christian crosses, gigantic emotional support pickup trucks, bizarrely aggressive patriotic bumper stickers, Trump signs and flags, etc. Depending on where you are those sorts of things are accompanied by very clear signs of deep poverty (mobile homes, trash-strewn lawns, run-down houses), but they can just as often be on or around very well-kept houses on huge acreage.

• And if you mean "culture" in the sense of theater, music, etc., you're unlikely to find any at all near a state border.

I guess the other thing is that Google Maps will tell you "Welcome to (state)" when you're navigating. There are some times that that's the only way you'll know.