Problem

The Beanie database documentation still showed motor.motor_asyncio.AsyncIOMotorClient, but recent FastAPI Users / Beanie installations use PyMongo's native async client. This made the Beanie setup guide and examples look outdated.

Fixes #1559.

Solution

• Replace Motor imports with pymongo.AsyncMongoClient in the Beanie documentation snippets.
• Apply the same update to the Beanie and Beanie OAuth examples so the full examples stay consistent with the docs page.
• Update the Beanie database guide wording and snippet highlight line numbers to match the shorter client setup.

Verification

• ruff format --check docs/src/db_beanie.py docs/src/db_beanie_oauth.py docs/src/db_beanie_access_tokens.py examples/beanie/app/db.py examples/beanie-oauth/app/db.py
• ruff check docs/src/db_beanie.py docs/src/db_beanie_oauth.py docs/src/db_beanie_access_tokens.py examples/beanie/app/db.py examples/beanie-oauth/app/db.py
• python -m compileall docs/src examples/beanie/app examples/beanie-oauth/app

I also ran uv run --with mkdocs --with mkdocs-material --with mkdocs-mermaid2-plugin --with markdown-include --with pymdown-extensions --with pygments --with mike mkdocs build --strict. The docs rendered, but strict mode failed on existing warnings unrelated to this change: deprecated Material emoji config, missing old migration links, and missing anchors.