Worth is determined by what some team would pay you on the open market.
It doesn't matter if White is (or is projected to be) only the 3rd or 4th best player on a team, what would it cost to get him on the open market, what is a team willing to pay?
Philly gave 33 year old Al Horford a starting salary of $28m against a $109m salary cap. That's 26% of the cap.
Milwaukee gave 31 year old Jrue a starting salary of $30m against a $112m salary cap. That's 27% of the cap.
Miami gave 35 year old Kyle Lowry a starting salary of $27m against a $112m salary cap. That's 24% of the cap.
Call it an overpay, but that's the championship tax contenders are willing to pay for marginal improvement to their championship odds.
On the flip side, 29 year old Fred VanVleet just got $40m against a $136m cap to be a top player on a rebuilding team. That's 30% of the cap.
So here we have White. A bigger (6'4") All-D combo guard, and as a baseline can give you 15/5/4/1/1 with 90% (FT) and 40% (3P) shooting splits (and that's at under 33 mins a game, per 36 looks even better). He's a minimal injury risk, with 0 chemistry or public image concerns, an advanced stats darling that you hope could put up even better stats in a bigger role, but also doesn't need the ball to be effective, and would likely fit in any system. Every possible thing a front office could look at for a non-superstar, he checks the box for.
I could see both contenders looking to get over the hump, and rebuilding teams looking for a good player to put next to a budding superstar going after White.
When White's a free agent (2025-26), the cap is expected to be $155.1m, and 25% of that cap is $39m. It all depends on which teams have cap room, but I'd expect White to get an offer of ~$40m (at least).
The Celtics might not pay him that, but I think some team would, so that's his worth.