Discussion: #10370 (This PR implements a planned item from the official roadmap)

Description

This PR implements the following item from the official roadmap (#10370):

• Docs for liveness and readiness for Kubernetes and others.

It adds a new page docs/en/docs/deployment/kubernetes.md to guide developers on configuring Kubernetes probes for FastAPI.

What it covers:

• Core Concepts: Explanation of Startup, Liveness, and Readiness probes and how they interact with FastAPI's lifespan startup phase.
• FastAPI Code Examples:
  • Basic health check endpoint configuration (docs_src/kubernetes/tutorial001.py).
  • Production-ready sample (docs_src/kubernetes/tutorial002.py) demonstrating separate /healthz and /readyz endpoints, database connection checks, and a custom logging.Filter to prevent Uvicorn log spam from frequent health check requests.
• Kubernetes Manifest (YAML): A standard deployment manifest snippet showcasing how to map the endpoints to startup, liveness, and readiness probes.

Checklist

• This PR links to a GitHub Discussion for the proposed code change.
• The documentation explains the change if needed.