Add suitbuilder backend improvements and SSE streaming fix

- Add dedicated streaming proxy endpoint for real-time suitbuilder SSE updates
- Implement stable sorting with character_name and name tiebreakers for deterministic results
- Refactor locked items to locked slots supporting set_id and spell constraints
- Add Mag-SuitBuilder style branch pruning tracking variables
- Enhance search with phase updates and detailed progress logging
- Update design document with SSE streaming proxy fix details

Co-Authored-By: Claude Sonnet 4.5 <noreply@anthropic.com>

docs/plans/2026-01-30-suitbuilder-design.md

@@ -222,3 +222,31 @@ No changes needed - ItemPreFilter used at line 969.
 | Task 5: Add Armor Level Scoring | ✅ Complete | Added armor_score = total_armor // 100 |
 | Task 6: Add Item Pre-Filtering | ✅ Already Working | No changes needed |
 | Task 7: AccessorySearcher | Not Started | Future |
+| Task 8: Fix SSE Streaming Proxy | ✅ Complete | Added dedicated streaming endpoint in main.py |
+
+---
+
+## Bug Fixes Applied
+
+### SSE Streaming Proxy Fix (2026-01-30)
+
+**Problem:** The generic inventory proxy at `/inv/{path:path}` used `httpx.request()` which buffers the entire response before returning. For SSE streams like suitbuilder search, this caused:
+- No progress updates reaching the frontend
+- "Gateway Time-out" after buffering the full 5-minute search
+
+**Solution:** Added dedicated streaming proxy endpoint `/inv/suitbuilder/search` in `main.py`:
+```python
+@app.post("/inv/suitbuilder/search")
+async def proxy_suitbuilder_search(request: Request):
+    async def stream_response():
+        async with httpx.AsyncClient.stream(...) as response:
+            async for chunk in response.aiter_bytes():
+                yield chunk
+    return StreamingResponse(
+        stream_response(),
+        media_type="text/event-stream",
+        headers={"X-Accel-Buffering": "no"}  # Disable nginx buffering
+    )
+```
+
+**Result:** Suits now stream to frontend in real-time with scores visible as they're found.