versioning: how do you handle breaking changes?

Hey everyone, I'm working on an API for a new service and we're starting to think about versioning. We want to make sure we can evolve the API without breaking existing clients. What are your go-to strategies for API versioning? Do you prefer URI versioning (e.g., /v1/users), header versioning (e.g., Accept: application/vnd.myapp.v1+json), or something else entirely? I'm curious about how you manage backward compatibility and deprecate old versions gracefully.