Isn't this an easy one?
Coaching upheaval. Udoka out at the last minute who had brought in several of his own guys, replaced by Mazzulla who was not a Udoka guy (who many view as not ready), already down 1 key assistant (Hardy), lost another mid year (Stoudamire), leaving Mazzulla to lead a bunch of Udoka guys who were probably not at all happy about the situation. The easy surface answer is Mazzulla wasn't ready, but I think really it's a lot deeper and more complicated than that (because even if he was ready, that's just a terrible situation to step into).
Injuries. Rob Williams was not Rob Williams of 2022 (really his only healthy season). Brogdon got injured (Game 2 against the Heat I think), went from averaging 15.6 and being +90 in the playoffs, to averaging 0.5 and was a -36 over final 5 games (sitting out 1 completely) shooting 1-16. And then Tatum sprains his ankle like 1 minute into Game 7.
Also I suspect now that Brogdon (despite winning 6MOY) was a little more disgruntled than he let on. Add to this the contract situation of others in '23: Brown, Pritchard had extensions coming up, Grant Williams was a free agent. All this impacts team chemistry.
Despite what went wrong, maybe a Tatum or Brogdon injury away from the Finals.
And some of what went right the next year is positive growth from Tatum/Brown (trading Smart and to a lesser extent Rob was probably a wake up call that this is a business, and helped force them to step up). They weren't the first young team to get to the Finals in and not return the following year ('86 Rockets w/ Hakeem/Sampson, '95 Magic w/ Shaq/Penny, '99 Spurs w/ Duncan, '01 Sixers w/ Iverson, '06 Heat w/ Wade, '07 Cavs w/ LeBron, '12 Thunder w/ Durant/Westbrook/Harden/Ibaka, etc. and we see other more-in-their-prime superstars like Duncan, Dirk, Giannis, Jokic) unable to make it back in consecutive years). And just a better fit with Holiday/Porzingis (vets happy with their role) and other growth (Pritchard/Hauser), and a full, prepared coaching staff.