The Bruins, per capgeek have something on the order of $2.8m in free space for 2022-23. Assuming they can get Bergeron to come back for $2-3m in salary and ~$2.5m in bonuses, they'll still need to fill that hole at 2C with 0 free agency dollars available. Neither Coyle or Haula is, in my opinion, a contender-type 2C. They both have positive qualities and are decent downstream in the bottom six, but really can't muster offense commensurate with Hall/Pastrnak on the 2nd line.
Lazar is probably gone. He's a very good 4C/W and deserves more than the baseline amount Boston can pay him. Blidh, too - though that is decidedly less of an issue since he's a possession anchor. With 13F (including Bergeron) and 8D (including re-signed Zboril) the B's will have to make some seriously hard choices.
First off, they MUST re-sign Bergeron. If he doesn't come back, there's no reason to bother with anything else. He's still an elite-elite two-way center and there's no one to replace him if he goes. Getting even a solid C replacement like RNH would be putting a band-aid on a massive wound.
Secondly, the B's MUST extend Pastrnak. He's probably going to ask for 8y, $80m at least but you've gotta do it because losing him for nothing as a UFA in thirteen months is a horrific prospect. If I'm Sweeney, I have to avoid the Tavares scenario at all costs and just bite the bullet on this one. If he's asking for McDavid money, you probably have to entertain trading him.
If either of the two aforementioned situations is not completed, the Bruins should just pack it in. They could contend for a postseason berth but not much beyond. But if the two previous problems are solved, you go for the 2C and push all your chips forward.
The package I'd offer for a 2C is Grz + JDB. Grzelcyk because he's got years remaining on a very palatable as an elite transition D (and spot PP QB) and Jake because he's a still-young 20-25 goal guy with great wheels. Maybe you toss in the 2023 1st and the '22 2nd as sweeteners (or Lorhei) but you have to 100% get a player who's dynamic offensively and hope that Lysell is close to being ready for prime time as a top-9 RW.
What does that get you? Maybe RNH. Probably not Miller or Scheifele. Same goes for Barzal. 'Zona needs Keller and Schmaltz if they're going to build toward something in the near future. Dylan Strome might be available but I'd be more comfortable with him in a bottom-six/pp role than centering two all-stars.
Basically, the players that would represent a significant upgrade at C are in all likelihood not moving barring a really significant overpay... and the ones that are available in the trade market, I don't see as anything beyond modest upgrades.
The course that MIGHT work (again if Bergeron is re-signed and Pastrnak is extended) is trading away a decent amount of cap to gain draft/prospect capital then going after one of the veteran C's that will probably hit UFA (Kadri, Copp, Stastny). As offensive players, they'd all be upgrades on Coyle and Haula... though the hit's they'd command would be unfortunate.
It's not an ideal situation. Two dominoes have to fall that I don't see as surefire locks (the Bergy/Pasta situations)... then the B's need some team looking for depth to move a 1/2 offense-first C for a #3LD and a #2LW (+ some extraneous pieces) ... OR ... dump cap and hope you don't overpay for a Kadri.
Anyway, sorry for the excessive text.