Looking at 3-point percentage outside the context of a particular offensive ecosystem is...odd. James Harden is also a career 36.5% shooter, identical to Hayward, but he'd shoot way above that if he were getting the looks Hayward gets in this Boston offense. In Utah, Hayward was the primary creator on a pretty grind-y offensive team--were not talking about tons of catch and shoot looks here.
He's obviously not Steph Curry, but his shooting this year was WAYYYY below what you'd expect, given the quality of looks he was getting. It's reasonable for people to expect him to be significantly better.
As for his shooting, one thing we know is that GH worked extensively on his shooting stroke while his leg healed. I wouldn't be surprised if his 3P% was to be on the high side of his career.
He is also getting a ton more wide-open shots in Brad's system. I posted his 2018-19 breakdown last week and going to repeat them (with updates and comparison to 2016-17 Utah). According to NBAstats.com:
In 2018-19, GH has shot 1 3Ps with a defender between 0-2 feet away (he made it); 4 3Ps with the defender 2-4 feet away (he's shooting 25% on these); 50 shots with the defender 4-6 feet away (24% on those); and 135 shots are wide open and he's only shooting 37% on these.
In 2016-17, GH shot 8 3Ps with a defender between 0-2 feet away (he made 50%); 44 3Ps with the defender 2-4 feet away (29.5%); 134 shots with the defender 4-6 feet away (46.3%); and 187 3Ps with the defender over 6' away (37.4%).
Perhaps more telling, of the 3P shots he has taken this year, 71.1% are wide-open and 97.3% of these are open or wide open. In Utah, those numbers were 50.1% wide-open and 86.1% open or wide-open.
And comparatively, with players who have taken > 125 wide open 3Ps, GH is 21st from bottom, trailing such shooters as Marc Gasol (37.2%), Al Horford (37.3%), Brook Lopez (38.0%), KAT (38.2%), Justice Winslow (41.2%), MaMO (42.5%), and Reggie Jackson (43.8%).
The top 10 are: Curry (52.2%), Hield (51.8%), Joe Harris (48.2%), Danny Green (47.9%), Josh Richardson (47.8%), Shamet (46.0%), Ariza (45.9%), Malik Beasley (45.3%), Paul George (45.1%), and Wesley Matthews (45.0%).
Just for fun, bottom 5 = Kelly Oubre is last at 28.1%; Osman (29.8%), Embiid (30.8%), Olynyk (31.6%), and Trae Young (31.8%). KO being there is surprising.