Not much will change, honestly. Joe Brady was already the Bills' offensive coordinator and primary play-caller before his promotion — the wiki describes it as "status quo on offense" (from the Joe Brady page). So the structure of who's calling plays stays the same.
The bigger story is Pete Carmichael Jr. — brought in from Denver as the new offensive coordinator (not the play-caller). The Bills' 2026 outlook notes that Brady's offense will focus on pushing the ball downfield more aggressively than under Sean McDermott. That plus the trade for DJ Moore (a downfield outside threat) points to a more vertical passing attack.
One fantasy ripple worth watching: FantasyPros suggested on their channel that James Cook's pass-game utility could get unlocked in this setup — if Carmichael deploys him like Alvin Kamara in New Orleans, Cook could add 200–300 receiving yards on top of his rushing production.