Based on what you said, the update to Local v6.6 is the difference - I realized I linked the wrong forum post! Here is what I meant to link: 502 Bad Gateway (nginx/1.16.0) in all sites after update - #12 by austinwendt
Which version of PHP are your sites running? I would try running through these steps - 502 Bad Gateway (nginx/1.16.0) in all sites after update - #35 by austinwendt - as it fixed the issue for a user with the same problem.