ci: remove playwright browsers caching

[afuetterer]

Description

The caching of the playwright browsers does not work as expected. It just creates a new cache with every CI run and fills up the GitHub Actions cache. The playwright docs actually do not recommend caching the browsers.

So let's remove this step.

Types of Changes

• Other (please describe): CI

Checklist

• I have read the contributor guide.
• My code follows the code style of this project.
• All new and existing tests passed.