This is mainly because the Bucks' team doctor has very much experience in treating Achilles tendon ruptures as well as excellent medical skills. And Durant has had this team doctor perform surgery on himself before. So the two sides have built up very much trust, so it makes perfect sense that Durant chose to work with the Bucks' medical team in the first place and let the Bucks' team doctor do the surgery for himself.
Many people will link the matter of the Bucks team doctor treating Durant's injury with Durant joining the Bucks. However, there is not much connection in between, this is mainly because the Bucks' medical level is very famous in the whole country. And the Bucks' team doctor has a lot of experience in treating Achilles tendons, for example, he once treated Big Lopez for an Achilles injury. Even Durant himself had him perform surgery on him, and the two sides have built up a lot of trust. Of course even more so because Durant is a New Yorker and can heal more in his hometown in the off season, which is all good.
Certainly can't rule out Durant joining the Bucks because of this. Because of Durant's injury, he won't be able to play in the NBA for a year or less. So in order to better treat the injury, of course, also want to play in their hometown team, so join the Bucks is a good choice. What's more, the Bucks also recruited Irving, recruiting very good players for themselves, making the Bucks very competitive in the next few seasons.
Of course we also see that Durant is also trying to prove himself, that's why he chose such a slow recovery time. And also to be able to get himself in a better shape to play. Also to prove himself to all the fans. He can lead a team to victory and win the championship.