Use UI snapshot testing to generate docs screenshots

### Body

It is always a pain to manually update screenshots whenever we make a UI change.
We also need to expand our test coverage.

Let's combine snapshot tests to generate images for each of our docs screenshots. We will need to list out all of the screenshots we generate, figure out if we're rendering a full page or a single component, and mock all API requests that view uses. The mock data will need to reflect real example use cases.

Vitest snapshots: https://vitest.dev/guide/snapshot

### Committer

- [x] I acknowledge that I am a maintainer/committer of the Apache Airflow project.

Start with the Vitest snapshot guide and inventory every documentation screenshot the project generates. For each screenshot, identify whether it renders a full page or component and which API requests need realistic example mocks; done means the documented screenshot set is covered by snapshot tests and can be regenerated automatically.

Written by the indexing model from the issue text.