feat: add minimum fastapi exception capture repro case

playgrounds/fastapi-exception-capture/USAGE.md

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+# FastAPI Exception Capture Usage
+
+Minimal reproduction of PostHog exception capture issue.
+
+## Quick Start
+
+```bash
+cd posthog-python/playgrounds/fastapi-exception-capture
+export POSTHOG_API_KEY="your_key"
+uv sync
+uv run python app.py
+```
+
+## Test
+
+```bash
+curl http://localhost:8000/test-exception
+```

playgrounds/fastapi-exception-capture/app.py

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+#!/usr/bin/env python3
+
+import logging
+import os
+
+from fastapi import FastAPI
+from fastapi.responses import JSONResponse
+from posthog import Posthog
+
+logging.basicConfig(level=logging.INFO)
+logger = logging.getLogger(__name__)
+
+app = FastAPI()
+
+POSTHOG_API_KEY = os.getenv("POSTHOG_API_KEY", "phc_PLACEHOLDER_KEY")
+POSTHOG_HOST = os.getenv("POSTHOG_HOST", "https://us.i.posthog.com")
+
+
+@app.exception_handler(Exception)
+async def global_exception_handler(request, exception):
+    client = Posthog(
+        POSTHOG_API_KEY,
+        host=POSTHOG_HOST,
+        log_captured_exceptions=True,
+        debug=True,
+    )
+
+    user_id = "anonymous"
+    properties = {"url": str(request.url)}
+
+    capture_id = client.capture_exception(
+        exception,
+        distinct_id=user_id,
+        properties=properties,
+    )
+
+    logger.info(
+        f"Captured exception: {exception.__class__.__name__} ({str(exception)[:100]}), id: {capture_id}"
+    )
+
+    return JSONResponse(
+        status_code=500,
+        content={
+            "error": "Internal server error",
+            "capture_id": capture_id,
+        },
+    )
+
+
+@app.get("/")
+async def root():
+    return {"message": "PostHog Exception Capture Playground"}
+
+
+@app.get("/test-exception")
+async def test_exception():
+    raise Exception("TEST BACKEND EXCEPTION")
+
+
+if __name__ == "__main__":
+    import uvicorn
+
+    print("Starting server...")
+    print(f"PostHog Host: {POSTHOG_HOST}")
+    print("\nTest: curl http://localhost:8000/test-exception")
+    uvicorn.run(app, host="127.0.0.1", port=8000, log_level="info")

playgrounds/fastapi-exception-capture/pyproject.toml

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+[project]
+name = "fastapi-exception-capture-playground"
+version = "0.1.0"
+requires-python = ">=3.9"
+dependencies = ["fastapi>=0.104.0", "uvicorn[standard]>=0.24.0", "posthog"]
+
+[tool.uv.sources]
+posthog = { path = "../..", editable = true }