Description

Improve Playwright test patterns in specs/variable.spec.ts and related page object to align with Playwright Best Practices.

This PR focuses on improving test patterns only.
It does not change test coverage or behavior.

Checklist

• page.waitForFunction() with DOM queries → locator-based waiting
• page.waitForTimeout() → state-based waiting
• waitForLoadState("networkidle") → wait for specific UI state
• Manual assertions → web-first assertions
• page.evaluate() for DOM manipulation → observe UI state instead
• CSS :has-text() → user-facing locators
• flaky check

Scope

This issue covers improvements in:

• specs/variable.spec.ts
• pages/VariablePage.ts

Use case/motivation

No response

Related issues

Part of #63036

Are you willing to submit a PR?

• Yes I am willing to submit a PR!

Code of Conduct

• I agree to follow this project's Code of Conduct