✨ Auto-generate OpenAPI servers from root_path (#1596)

* root_path included in servers object instead of path prefix

* ♻️ Refactor implementation of auto-including root_path in OpenAPI servers

* 📝 Update docs and examples for Behind a Proxy, including servers

* 📝 Update Extending OpenAPI as openapi_prefix is no longer needed

* ✅ Add extra tests for root_path in servers and root_path_in_servers=False

* 🍱 Update security docs images with relative token URL

* 📝 Update security docs with relative token URL

* 📝 Update example sources with relative token URLs

* ✅ Update tests with relative tokens

Co-authored-by: Sebastián Ramírez <tiangolo@gmail.com>

docs_src/behind_a_proxy/tutorial004.py

@@ -0,0 +1,15 @@
+from fastapi import FastAPI, Request
+
+app = FastAPI(
+    servers=[
+        {"url": "https://stag.example.com", "description": "Staging environment"},
+        {"url": "https://prod.example.com", "description": "Production environment"},
+    ],
+    root_path="/api/v1",
+    root_path_in_servers=False,
+)
+
+
+@app.get("/app")
+def read_main(request: Request):
+    return {"message": "Hello World", "root_path": request.scope.get("root_path")}