Based on his past salaries, he is not making big money anymore, so I understand the decision.
https://hoopshype.com/player/patrick-beverley/salary/Based on the news,
Beverley agreed to a two-year, $4 million deal with Hapoel Tel Aviv,
sourceSo he is already secured with that salary, plus he will earned heavy minutes, unlike playing with the NBA where he will just be in the bench.
I think he still want to really show his value and at this stage, it's best to show it overseas.
NBA players usually go overseas only if they don't get acceptable offers from NBA teams, i.e. they are not needed in the NBA. So that 4 million dollar contract is a good deal for him, considering he is already 36 years old.
p.s.
Maybe no one in the NBA likes Beverley, but I think he has good defensive skills, and he clearly deserves the veteran minimum.