I think Keiths' numbers are a bit off, he started Jaylens' salary a bit too high in an extension.
This is what I think he'd be leaving on the table if he signed a 2+1 extension with Boston before this season.(going off of Keiths 143M cap projection for 24/25)
If he extends now, he'd make 34.2M in 24/25 and 37M in 25/26, with his option for 39.8M in 26/27. He'd also have 8.3M in incentives in the first two seasons, around 5.5M that he can reasonably make.
If he wait til FA, he'd make 42.9M in 24/25 and 46.3M in 25/26.
So to lock in 111M in security early, he'd be leaving 18M guaranteed over the first two years, but would probably make 5.5M of that up in incentives.
So leaving somewhere between 12.5M to 18M on the table to lock in 111M.
One big benefit to signing a 2+1 now is, the second year of that extension would be his tenth year in the NBA. Opting out then would make him eligible to sign a 35% max, instead of a 30% max in 24/25 if he doesn't extend, and would come after the new TV deal kicks in. He'd probably make up most of the difference of the money he left on the table in the 26/27 season alone. (That's assuming he would sign a 3+1 or 4+1 max in 24/25 if he doesn't extend now)
I thought before this playoff run, that him signing an extension now was at least a decent possibility. I think making the finals probably knocked that way down. Just being in that high profile spot, probably gives him a small step up in being in voters minds for all-NBA next season. If he has a similar season next year as he did this year, maybe he gets a vote in a close race with a Donovan Mitchell or Paul George that he wouldn't have if they lost to Milwaukee. It's probably enough for him to gamble on trying to make all-NBA and be eligible for an early motherlode from Boston.
I'd guess now the only way he extends before this season is if he really wants to be here, and the Celtics said to him that if he wouldn't extend that they'd be afraid he was going to walk and were going to trade him now. I'd consider that a very unlikely scenario.