It's a center-entry or central hall, not a foursquare; in a foursquare you always enter into a stair-hall that is a corner room, and the front door is to one side or the other.
This house is quite stark; there are only three style markers: the repeated use of segmental arches (windows and porch) the generous roof overhangs, and the bullseye window with keystones. The overhanging eaves are a nod toward the arts & crafts bungalow period which was drawing to a close in 1924. The flat arches are seen in several different periods, but here when coupled with the bullseye window, I believe the builder may have been influenced by the Beaux-Arts movement. But 1924 is very late for that as well. Perhaps it's in a very architecturally conservative area.If the interior trim carries forth a fancier and delicate classically-inspired theme, then I'm right, but it could as easily have heavy dark Craftsman detailing. You're the only one who can tell.
If you replace the windows now, rest assured they will need to be replaced again within 20 years; if you rehab the originals, they can last another two lifetimes.
Casey

"Foursquare" was a layout, not an independent style. You can have Craftsman, Spanish Colonial, farmhouse and even "Victorian" foursquares. It depends on the trim details.

Looks nice - the key to "foursquare" is the definite split into a 4-quadrant layout, although some of them merged two quadrants to get a large living room/dining room combo.

I've seen some with a center entry that went into a central staircase. More common was a folded staircase to one side with the landing sticking out a bay window ... gave light and saved on floor space.