Would it make sense to maintain separate sets of Pact stages for each branch?

I’m not sure I entirely follow. The concept of “branches” are there to map changes for a given branch. Are you using

pact-broker record-deployment

when you deploy to each environment?

I’ve observed that when a webhook is triggered, the verification always runs against the main branch (staging), regardless of which branch initiated the process. This could potentially cause issues when the branches diverge.

When a webhook fires, it specifies in the payload which version (and branch/environment) that it needs to check against. Your webhook target should read the value of that body, and checkout the correct code accordingly. See also https://docs.pact.io/pact_broker/webhooks#using-webhooks-with-the-contract_requiring_verification_published-event