Improve Playwright test patterns in providers.spec.ts

[hussain-s]

Summary

Improve Playwright test patterns in providers.spec.ts and ProvidersPage.ts without changing test coverage or behavior.

What changed

• replaced DOM-query based waiting with locator-based readiness checks
• moved Admin menu navigation into the page object
• replaced manual row-count and string assertions with web-first Playwright assertions
• kept the existing providers test coverage intact

Validation

• pnpm exec eslint tests/e2e/specs/providers.spec.ts tests/e2e/pages/ProvidersPage.ts
• pnpm exec tsc --noEmit -p tsconfig.app.json
• TEST_USERNAME=admin TEST_PASSWORD=admin AIRFLOW_UI_BASE_URL=http://localhost:28080 pnpm exec playwright test tests/e2e/specs/providers.spec.ts --project=chromium

Relates to #63431

[boring-cyborg]

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[Shrividya]

Nit: The original waitForTableData() specifically checked for "tbody tr td a" links to distinguish real data from skeleton rows. In this line, the check would pass as soon as it identifies ,even before the real data loads.

[hussain-s]

Good catch. I tightened waitForLoad() so it now waits for the first provider link to be visible, not just the first row shell. That keeps the readiness check tied to real table content while staying locator-based.

[Shrividya]

LGTM! 👍