I think you’re quite possibly right about the Yankees pursuing Seager, especially because they could easily shift him to third in another year or two when Anthony Volpe hits the majors. Rizzo I’m not so sure about; depends on what the market’s like for him. NY’s already got several big long-term commitments to players over 30 (Stanton, Cole, and LeMahieu) and presumably will be adding Judge, who turns 30 next year, to that list.
On a league-wide scale there’s the whole impending CBA issue—another factor that could influence the market for free agents (let alone have a potentially damaging impact on the 2022 season in general). I don’t know enough about it to make a prediction, except to say that it probably won’t be pretty.