Your theory makes sense. Not that dissimilar to the idea that the advantage tilts to the hitters the longer a playoff series goes because they've seen all the pitchers 2-3 times by game 6-7. I recall Schilling making a point of not pitching against any divisional opponents in spring training so they wouldn't get bonus looks at him.I'm sure you could find this data somewhere, but I would guess that pitchers in general pitch worse against their own division. When you see a guy 4-5 times instead of 1-2 times over a season you're going to have a better idea of what he throws and how to hit him.
Part of it also has to be that as we know the AL east is just better than other divisions. Over 2021 and 2022 those 8 teams combined for a 105 ops+
Just another reason the more balanced schedule next year is a benefit. Of course, that goes for other AL East pitchers against Sox hitters too.