This seems like a cool problem.
There is a difficulty: the 40% over 1,507 attempts can itself be thought of as a certain probability outcome assuming a certain "true" 3-pt. shooting percentage (which others have kind of alluded to). And that will influence the answer to the problem. So for example: if Tatum is a "true 37%" shooter from three, there is a certain chance (say 12%) that over those 1,507 attempts, he will make 40% of them. Or he could be a "true 41%" shooter from three who happened to shoot a bit more poorly over 1,507 attempts. But the answer to the second part of the question depends on whether he's a "true 37%" or 41% or whatever percent shooter.
So I think to answer you'd have to make an assumption, and the easiest one to make is that he's a "true 40%" shooter, with those 1,507 attempts as evidence (which is certainly much better evidence than a couple of hundred attempts).
From there, I think I'd do a Monte Carlo simulation (there are probably some online), where you'd run 344 outcomes, with a 40% chance of each individual one being "hit" and the others being "miss." If you did a Monte Carlo with 20,000 runs (of 344 outcomes each) say, that should give you a pretty good sense of how often he lands at 31.7%. It might be useful to break the results into bands, so you could see e.g. what percentage of time he hit 31% to 32%, 32% to 33%, 33% to 34%, etc. Some thoughts ... I might look into this later if I have time. It is interesting.