This comparison is probably closer than we think:
Top "freely available relievers" 2022:
BOS (Whitlock, Schreiber, Strahm, Sawamura, Ort, Davis, Danish, Kelly): 341.2 IP, 3.45 FIP, 42.8 GB%, 23.9 K%, 87 FIP-
TBR (Springs, Adam, Poche, Raley, Wisler, Fairbanks, Kittredge): 358.1 IP, 3.26 FIP, 37.9 GB%, 27.2 K%, 86 FIP-
Now, that excludes several clunkers in our pen (Robles, Familia, Diekman, et al.) and theirs (Yarbrough, Garza, Faucher, Mazza, et al.). But playing around with those guys is the cost of having a bullpen, whether you're playing scrap heap relievers or outbidding for free agents (Ian Kennedy, Steve Cishek, Jake McGee, Jake Diekman, Will Smith).
I think there's a difference in that our bullpen is built around home run suppression, which it's alright at (12th of 30 teams). Tampa relievers struggle in that department (22nd of 30 teams) but can strike more guys out.
Besides that, the major issue seems to be defense. The 2022 Sox pitching staff has the second-worst gap between ERA and fielding independent pitching stats in all of MLB. The Rays have the best (most favorable) gap. With Casas up and Kiké replacing Duran in center field, I expect our bullpen next year will be a lot "better" in that regard.