Generate a mermaid diagram for the database ERD schema

### Description

The docs currently show Airflow's database ERD schema as an image: https://airflow.apache.org/docs/apache-airflow/stable/database-erd-ref.html. To make this searchable, it would be useful to visualize this using mermaid, which also supports ERD schemas: https://mermaid.js.org/syntax/entityRelationshipDiagram.html.

### Use case/motivation

Would be useful to make text in the database diagram searchable.

### Related issues

_No response_

### Are you willing to submit a PR?

- [ ] Yes I am willing to submit a PR!

### Code of Conduct

- [X] I agree to follow this project's [Code of Conduct](https://github.com/apache/airflow/blob/main/CODE_OF_CONDUCT.md)

Start with the database ERD reference page linked in the issue and compare its current image-based schema with Mermaid's entity relationship diagram syntax. Done means the ERD is represented as searchable Mermaid text in the documentation while retaining the schema relationships shown by the existing diagram.

Written by the indexing model from the issue text.