Almost certainly they do not...
Unless, as previously discussed, we can't get any of Springer/Bauer/Tanaka/Lindor/Kim etc. Then we sign Realmuto and trade Jansen or Kirk plus a SP prospect plus one more player for Snell and a member of the Rays 98 mph bullpen club
Soto could easily be the best hitter in baseball for the next decade. But Trout and Betts provide value in areas he won't. Kinda how Miggy was the best hitter in the game for a while even while Trout was more valuable overall.
Yankees are smarter than that. If they don't re-sign him it's because of some combination of cost constraints and concerns about his health
Sounds like Lemahieu is their priority and they might not be able to afford much after that if they pay him what he's worth
Some good points
I'm all for signing Springer and using Gurriel/catchers as trade chips to aquire a top of the rotation starter
Trading for Lindor or Arenado should perhaps be plan B anyway, OR the icing on the cake if you've already improved at SP 2 and CF
Whatever you do, don't accidentally Google "george springer blue jays" like I just did
Some of the "articles" that come up sound ridiculous and I don't dare click on them
Advantages of trading for him now:
1. He plays for you at age 27 in 2021 during a year you want to contend
2. You have a full year to negotiate a contract extension with him during which time no other team is allowed to negotiate with him
3. If he plays one year for you and walks you get draft pick compensation because guaranteed he'll be given the qualifying offer and reject it.
4. Excitement continues to build for fans and potential free agent recruits