Setting aside personnel for a minute, the single most important offseason move will be to fix this Offensive/Special Teams/Offensive Line coaching situation. If they don't do that, it won't matter what magical players they bring into camp.
Setting aside personal bias and hyperbolic overreaction to this season, here is the depth chart featuring players the Patriots already have under contract for 2023. Below that is a list of their free agents according to age and position. This matters more than who you think is "good" or needs replacing. HELP indicates where there is a clear need either by draft pick or free agent. I also crossed out players I think suck or won't help... I didn't say I was setting aside personal bias... it's my list.
OFFENSE
QB – Mac Jones, Bailey Zappe, Brian Hoyer (PS/Coach)
LT – Trent Brown, HELP
LG – Cole Strange, Chasen Hines
C – David Andrews, Kody Russey,
RG – Michael Onwenu
RT – HELP, Andrew Stueber
TE – Hunter Henry, Jonnu Smith, HELP
RB – Rhamondre Stevenson, Kevin Harris, HELP
HB – Pierre Strong, Ty Montgomery,
BIG WR – DeVante Parker, Kendrick Bourne, Raleigh Webb
FAST WR – Tyquan Thornton, HELP
SLOT WR – HELP
DEFENSE
DT – Christian Barmore, Lawrence Guy, Davon Godchaux, Sam Roberts
DE – Deatrich Wise, DaMarcus Mitchell
SLB – Matthew Judon, Anfernee Jennings, Ronnie Perkins
MLB – Ja’Whaun Bentley, Josh Uche, Jahlani Tavai,
WLB – HELP
SS – Kyle Dugger, Adrian Phillips, Brenden Schooler,
FS – HELP, Joshuah Bledsoe
BIG CB – HELP, Jalen Mills, Shaun Wade
SLOT CB – Jack Jones, Marcus Jones,
SPECIAL TEAMS
K – Nick Folk, Quinn Nordin
P – Jake Bailey,
LS – Tucker Addington
GUN – Brenden Schooler, HELP
FREE AGENTS
Matthew Slater WR 37.2 UFA
Devin McCourty FS 35.3 UFA
Marcus Cannon RT 34.6 UFA
Jamie Collins LB 34.0 UFA
Cody Davis FS 33.5 UFA
James Ferentz C 33.5 UFA
Carl Davis DT 30.8 UFA
Joe Cardona LS 30.7 UFA
Conor McDermott T 30.2 UFA
Nelson Agholor WR 29.6 UFA
Jonathan Jones CB 29.2 UFA
Jabrill Peppers S 27.2 UFA
Raekwon McMillan ILB 27.1 UFA
Yodny Cajuste T 26.8 UFA
Jakobi Meyers WR 26.1 UFA
Kristian Wilkerson WR 26.0 UFA
Isaiah Wynn T 26.0 UFA
Damien Harris RB 25.8 UFA
Joejuan Williams CB 25.0 UFA
JJ Taylor RB 25.0 UFA
Tre Nixon WR 25.0 UFA
Myles Bryant CB 24.9 RFA
Mack Wilson LB 24.8 UFA
They desperately need some Offensive Tackles for the future, if there's a high draft pick or two ready to be used offensively it needs to be here. Trent Brown is the only tackle under contract. I'd spend a high draft pick, and bring another value vet free agent in along with Yodney Cajuste who they could sign for peanuts to an incentive laden deal where he only gets paid if he stays healthy. He's the only RT who played well out there this season but he can't stay healthy.
Like most seasons fans will focus on "weapons" because they think those automatically = offense... they don't. And frankly the Pat's weapons under contract are very good, they just look like crap because of the coaching situation and possibly having to start the backup QB over this year's starter.
That being said, they absolutely need a slot receiver in 2023 so they either bring Meyers back or hopefully Kristian Wilkerson if healthy fills that role. Either Way I'd bring back both Wilkerson and Nixon to camp, they're both good young players they've used resources to develop. Time for them to prove themselves in camp, or for the team to finally cut bait. They could use a mid to late round pick at WR to add some team speed as well.
They also need a young developmental RB in the chute to replace Damien Harris, RB is a position they should draft or find an UDFA every year. They should also take a TE if there's an athletic one of value sitting there in the mid rounds, they need some depth.
Defensively they desperately need a fast weak-side LB for the future and they could also use some size/speed at the CB position. Along with bringing Jon Jones back on a short deal (age), I would find a 1A alpha corner with great speed and agility. That would slide Mills to the 2 position and improve the defense mightily. They also need a Free Safety for the future, this being said I would focus entirely on big fast CB's so I could convert one to free safety. They have decent strong safeties, time to add to the size and speed in the defensive backfield.
The only free agents I’d consider bringing back would be Matthew Slater, Devin McCourty, Jamie Collins, Carl Davis, Joe Cardona, Jonathan Jones, Jabrill Peppers, Yodny Cajuste, Jakobi Meyers, Kristian Wilkerson, Damien Harris, JJ Taylor, Tre Nixon. James Ferentz I might make an assistant offensive line coach. The coaches have a better grasp on the guys too old to continue on, I'll defer to them on that.