feat: integrate branching into chat service and step creation

Add is_branching guard to unified_chat_service.send_chat_message() that
routes messages through BranchAwarePromptBuilder when a session has active
branching. Add branch_id to all AISessionStep constructor calls in
flowpilot_engine.py via optional branch_id param on _create_step_from_parsed.

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

backend/app/services/unified_chat_service.py

@@ -81,6 +81,54 @@ async def send_chat_message(
     if session.status not in ("active", "paused"):
         raise ValueError(f"Cannot send messages to a {session.status} session")
 
+    # If branching is active, route to branch message handler
+    if session.is_branching and session.active_branch_id:
+        from app.services.branch_manager import BranchManager
+        from app.services.branch_aware_prompt_builder import BranchAwarePromptBuilder
+        from app.models.session_branch import SessionBranch
+
+        branch_result = await db.execute(
+            select(SessionBranch).where(SessionBranch.id == session.active_branch_id)
+        )
+        branch = branch_result.scalar_one_or_none()
+        if branch:
+            manager = BranchManager(db)
+            sibling_ctx = await manager.build_cross_branch_context(branch.id)
+
+            builder = BranchAwarePromptBuilder()
+            session_context = f"Problem: {session.problem_summary or 'Unknown'}. Domain: {session.problem_domain or 'Unknown'}."
+            prompt_args = builder.build(
+                branch_messages=branch.conversation_messages,
+                sibling_summaries=sibling_ctx,
+                session_context=session_context,
+                attachments=[],
+                new_message=message,
+                revival_context=branch.evidence_description if branch.status == "revived" else None,
+            )
+
+            # Override images from prompt_args with actual images if provided
+            if images:
+                prompt_args["images"] = images
+            ai_content, input_tokens, output_tokens = await _call_ai(**prompt_args)
+
+            # Update branch conversation
+            msgs = list(branch.conversation_messages or [])
+            msgs.append({"role": "user", "content": message})
+            msgs.append({"role": "assistant", "content": ai_content})
+            branch.conversation_messages = msgs
+
+            session.total_input_tokens += input_tokens
+            session.total_output_tokens += output_tokens
+            session.step_count += 2
+
+            if session.status == "paused":
+                session.status = "active"
+
+            suggested_flows = extract_suggested_flows(
+                await rag_search(query=message, account_id=account_id, db=db, limit=8)
+            )
+            return ai_content, suggested_flows, session
+
     # Auto-title from first message if still default
     if session.step_count == 0 and message.strip():
         session.title = _auto_title(message)