test: add playwright pipeline and start migrating Cypress to Playwright

[susnux]

Summary

Problem

Cypress is always flaky this has two reasons:

1. Tests are bad
2. Cypress itself

For 2 we have cases where the electron renderer just crashes and this happens more often than you would think.
Also for 2 its a problem that Cypress runs within the browser tab, so you cannot test cross-tab communications.

Moreover Cypress has evolved from opensource to open core and nudging you to their paid services and especially they actively fight against community by making it impossible to create open source variants.
This does not really fit into a project with a strong sense for free software and open source.

Solution

Playwright offers a popular opensource frame work to create end to end tests with proper support for cross tab communication. Also it integrates very well with most IDEs and their post-test analysis is open source.

TODO

• Migrate more tests

Checklist

• Code is properly formatted
• Sign-off message is added to all commits
• Tests (unit, integration, api and/or acceptance) are included
• Screenshots before/after for front-end changes
• Documentation (manuals or wiki) has been updated or is not required
• Backports requested where applicable (ex: critical bugfixes)
• Labels added where applicable (ex: bug/enhancement, 3. to review, feature component)
• Milestone added for target branch/version (ex: 32.x for stable32)

AI (if applicable)

• The content of this PR was partly or fully generated using AI