I think there's three major things.
First is selling high. The Smart trade was cold, same with Timelord. Brad Stevens is very clearly unafraid to look at the players he drafted and evaluate them, and I think being really early to do that instead of late does wonders for trade value. I think a lot of Celtics fans saw Smart's regression from his DPOY year due to wear and being on the wrong side of the aging curve, but I don't think many FOs would have been so willing to trade their longest-tenured player and someone who means a lot to the franchise. By the time everyone's saying someone should be traded, it's too late: the best trades in hindsight are controversial at the time. I certainly hope that's true for these, and I trust Brad Stevens to know these guys better than anyone.
The other thing to note is that the Celtics FO clearly looks at a lot of analytics. Derrick White wasn't making too many waves at the deadline when we got him, but he had really good analytics behind him. Same with KP and Jrue, although obviously those players are more well-known. I don't know if the Celtics just trust their numbers more than other teams or have internal metrics that track more closely with the public ones, but if you want to know how the Celtics are gonna value players EPM or RAPM is a pretty good proxy.
The third thing is the win-win nature of a fair bit of these trades, even with some injuries. Nesmith and a pick for Brogdon is pretty reasonable. The Pacers are doing great letting Halliburton conduct the orchestra and can use Nesmith: they're also young enough to keep taking swings on draft prospects that can develop. Portland doesn't really need Jrue, but they can afford to have Timelord sit a season. Same with the Wizards trying to lose and not wanting to pay KP. I think the Celtics get an advantage by still having a lot of assets and being able to swoop in, but I think Timelord has solid future DPOY chances and Smart will do well in Memphis.
The only thing I find a little puzzling is how much value the Celtics seem to get out of their picks. Is the expected value of a Boston pick even a player who gets a roster spot? Unlike older teams I have a hard time believing Tatum is not playing heavy minutes in future seasons, and I just can't imagine the team drafting higher than 20 in the next couple of years.
It's important to remember what plus-minus stats actually measure. Box score versions measure your, well, box score, which is a lot more about shooting luck at this point in the season than anything else. Clearly Tatum is the 3rd best player on the team, right?
RAPM or EPM measure how good you are on your specific team in the mostly regular season minutes they play with and without you. Brown is not on a team that maximizes his potential, and especially as the Celtics have added more and more scoring his tools aren't necessarily being put to amazing use in the regular season. You don't need to take midrange shots if your offense is consistently getting great looks elsewhere on the floor. Players like Hauser and White can take better advantage of the advantages the Celtics get playing against teams that can't really stop them. You see the same thing for 3-and-D players on other really good teams: Mikal Bridges was an analytics darling for the Suns playoff runs.
How much does not being as efficiently dominant when your team has a +10 net rating as other players matter? It doesn't. It's a good thing to have players with underutilized talents in the regular season. I'm sure the Nuggets would love to have Jokic's numbers get worse, if it means that their non-Jokic lineups are better. Everyone on the Celtics is sacrificing their own stats right now, JB perhaps more than anyone, to win games and prepare for the playoffs.
In the playoffs, as defenses lock in and scoring gets tougher, you won't be able to feed the bigs dunks or feed the shooters with a ton of open looks. Who's gonna take advantage of the spacing and be able to score against the elite defenders in the postseason? IDK, maybe the guy who was the best player in the Finals for the Celtics. The guy who regularly plays against the opposing teams' best or second-best defender. The guy who can score from anywhere and has the physical tools to lock in on defense.