[ECO-2362] Fix flaky playwright tests

[xbtmatt]

Description

• [x] Check shadow dom elements by using getByRole
• [x] Fix some package.json commands that were incorrectly copy-pasted
• [x] Wait for elements to be visible more explicitly before expecting they are there

Testing

Playwright e2e tests.

Checklist

• [x] Did you update relevant documentation?
• [x] Did you add tests to cover new code or a fixed issue?
• [x] Did you update the changelog?
• [x] Did you check all checkboxes from the linked Linear task?

[vercel[bot]]

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Name	Status	Preview	Comments	Updated (UTC)
emojicoin-dot-fun	✅ Ready (Inspect)	Visit Preview	💬 Add feedback	Nov 5, 2024 1:16am
emojicoin-dot-fun-docs	✅ Ready (Inspect)	Visit Preview	💬 Add feedback	Nov 5, 2024 1:16am