Add playwright E2E tests

[samfreund]

Description

This adds playwright tests. These will test the frontend and the backend, by running both of them and simulating interactions with the frontend.

Meta

Merge checklist:

• Pull Request title is short, imperative summary of proposed changes
• The description documents the what and why
• If this PR changes behavior or adds a feature, user documentation is updated
• If this PR touches photon-serde, all messages have been regenerated and hashes have not changed unexpectedly
• If this PR touches configuration, this is backwards compatible with settings back to v2025.3.2
• If this PR touches pipeline settings or anything related to data exchange, the frontend typing is updated
• If this PR addresses a bug, a regression test for it is added

[Gold856]

Can we avoid data-testid? I don't like adding test-only things to code (although we are already doing that on the server). I would slightly prefer it if we could locate the elements in a different way.