CI: cleanup local integration workflow

[fangchenli]

Reference Issues or PRs

slipt #2075, prepare for cypress to playwright migration.

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?

[iameskild]

Great work @fangchenli!