BE: allow workflow run UI to show browser stream if workflow run has one (#3834)

skyvern/forge/sdk/db/client.py

@@ -1878,6 +1878,7 @@ class AgentDB:
         sequential_key: str | None = None,
         ai_fallback: bool | None = None,
         depends_on_workflow_run_id: str | None = None,
+        browser_session_id: str | None = None,
     ) -> WorkflowRun:
         async with self.Session() as session:
             workflow_run = (
@@ -1908,6 +1909,8 @@ class AgentDB:
                     workflow_run.ai_fallback = ai_fallback
                 if depends_on_workflow_run_id:
                     workflow_run.depends_on_workflow_run_id = depends_on_workflow_run_id
+                if browser_session_id:
+                    workflow_run.browser_session_id = browser_session_id
                 await session.commit()
                 await session.refresh(workflow_run)
                 await save_workflow_run_logs(workflow_run_id)

skyvern/forge/sdk/workflow/service.py

@@ -465,6 +465,10 @@ class WorkflowService:
         if browser_session:
             browser_session_id = browser_session.persistent_browser_session_id
             close_browser_on_completion = True
+            await app.DATABASE.update_workflow_run(
+                workflow_run_id=workflow_run.workflow_run_id,
+                browser_session_id=browser_session_id,
+            )
 
         # Check if there's a related workflow script that should be used instead
         workflow_script, _ = await workflow_script_service.get_workflow_script(workflow, workflow_run, block_labels)