fix(web): retain terminal PR badges after checkout switch - #4755

💭 This PR is about state management for snapshots, not UI styling, so the check should pass. But there's a tension here—the check defaults to failure and the instructions say to respond with just "All clear" when there are no findings, yet the response schema requires JSON with state, title, and summary fields. I need to figure out how to reconcile the text instruction with the structured format requirement. Let me do a quick scan of the actual changes to be thorough. The diff is mostly logic-focused, but I should verify there aren't any hidden UI consistency issues lurking in the component files being modified. Looking at ThreadStatusIndicators to see if it uses resolveThreadPr and whether it needs the same consistency updates, then checking ChatView around line 4131 to verify how it handles the provider when displaying the retained merged PR. Looking at how activeThreadPr is used in ChatView, it only passes state and number for display, not the provider itself. The PR pill in the header likely handles provider display separately. Since this change is purely state and logic with no UI components, CSS, or styling involved, there shouldn't be any consistency issues to worry about.