TST: playwright test for dask gateway

[fangchenli]

Reference Issues or PRs

close #1971

What does this implement/fix?

Put a x in the boxes that apply

• Bug fix (non-breaking change which fixes an issue)
• New feature (non-breaking change which adds a feature)
• Breaking change (fix or feature that would cause existing features not to work as expected)
• Documentation Update
• Code style update (formatting, renaming)
• Refactoring (no functional changes, no API changes)
• Build related changes
• Other (please describe):

Testing

• Did you test the pull request locally?
• Did you add new tests?

Any other comments?

requires #1996 and #2027 first.

Moving this from e2e to integration requires modification to CI. I'll keep it in e2e for this PR and address the CI changes in a separate PR.

[pavithraes]

From today's chat: we need to move the files to test_integration -- it's not running in CI yet but in-progress

[dcmcand]

@marcelovilla can you take a look at this PR and see if you can pick it up?

[marcelovilla]

I'll go ahead and close this draft PR as it has not seen any recent activity. I agree testing dask-gateway functionality is important and we'll work on implementing it using the dask API rather than Playwright.