Is it possible to update project settings using the v3 API? 

If not, is there any other way to programmatically change these settings?

Hi!

yes, it is possible to update some project settings via API. The API documentation includes a few examples for the projects endpoint that might be a good starting point:

https://www.openproject.org/docs/api/endpoints/projects/
https://www.openproject.org/docs/api/introduction/#openproject-api-introduction

Best

Alexander