Why he will end up with the Sox: He grew up a Sox fan. They miss Mookie's bat, JBJ is a free agent, and Benintendi's stock has slipped. They could certainly use some punch in the OF and Bloom has gotten the Sox about 35 million under the luxury tax thresh hold. NESN ratings were cut in half this year so ownership may want to bring in a big name. And, he's not just a big time player during the regular season, but also in the playoffs too, so you know he can handle the pressure of playing in Boston. Lastly, he and Cora were close in Houston. It's possible Cora returns to Boston once the WS is wrapped up.
Why he may not end up with the Sox: Bloom is from the Tampa Bay family tree. They believe in payroll flexibility (see Friedman with the Dodgers - I don't believe Friedman signed anyone to a big deal before the Betts signing). And, I believe the Sox may have to give up their second round pick (it's a high one in the 2nd round) if they sign someone who has been given a qualifying offer...which Springer almost assuredly will be.
Not sure Bloom - who is big on returning the Sox farm system back to one that can replenish the major league team - will want to do that. Especially when he looks at what the team he had a hand in building is doing right now in the 2020 postseason. He may just decide to stick to his process.
So, I'd close by saying if Dombrowski was the GM, there's no doubt the Sox would give Springer what he wants. With Bloom in charge though, who knows.