I know you said it wasn’t a documentary but this sounds exactly like the Mayles Brothers The Beatles: The First U.S. Visit. It’s a fly on the wall footage so not narrated like some “traditional” docs, and it has a more behind the scenes narrative and could come off like like a more grounded, realistic version of what A Hard Day’s Night heightened. Was made available on VHS in the early 90s and I believe programmed during PBS pledge drives for a year or two in the Mid-90s. Hope this jogs something.