Cleaned up login page loading in E2E tests

[EvanHahn]

towards https://linear.app/ghost/issue/NY-1000

This test-only change should have no user impact.

This change:

• Logs a more helpful error when visiting the signup page. This seems to be failing in CI a lot, and it'd be useful to know more about the error.

• Removes an unnecessary waitFor on the email address field. locator.fill() automatically waits for this.

• Stops an unnecessary check when going to the sign-in page. A user should already be available, and the extra wait will probably never happen--we visit a URL and then check that we're not at a different URL, which it will never be. (And if it did redirect, we wouldn't catch it this way.)

[coderabbitai]

Walkthrough

This pull request updates navigation handling across multiple page helper classes in the e2e test suite. The BasePage class's goto method now explicitly returns a Playwright Response object (or null) instead of void, with corresponding signature updates to child classes SettingsPage and PublicPage. Additionally, the LoginPage class is refactored to replace a multi-attempt wait loop with a single navigation call followed by explicit response validation, and removes an unused private field while reducing initial synchronization overhead.

🚥 Pre-merge checks | ✅ 3

✅ Passed checks (3 passed)

Check name	Status	Explanation
Title check	✅ Passed	The title accurately summarizes the main change: cleaning up the login page loading in E2E tests, which aligns with the core modifications across multiple test helper files.
Description check	✅ Passed	The description is directly related to the changeset, explaining the rationale for removing unnecessary waits and checks in the login flow, along with improved error handling.
Docstring Coverage	✅ Passed	No functions found in the changed files to evaluate docstring coverage. Skipping docstring coverage check.

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✨ Finishing touches

• 📝 Generate docstrings

🧪 Generate unit tests (beta)

• Create PR with unit tests
• Post copyable unit tests in a comment
• Commit unit tests in branch give-better-errors-when-login-fails-in-e2e-tests

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[coderabbitai]

Actionable comments posted: 1

🤖 Fix all issues with AI agents

In `@e2e/helpers/pages/public/public-page.ts`:
- Around line 80-93: In goto(), remove the redundant unconditional call to
enableAnalyticsRequests() so analytics are only enabled for the analytics
project; keep the call inside the if (testInfo.project.name === 'analytics')
block along with pageHitRequestPromise() and ensure the existing logic that
awaits pageHitPromise and returns result remains unchanged (references: goto,
enableAnalyticsRequests, pageHitRequestPromise, test.info()).