Fix MySQL container issue in Playwright E2E tests

[ryota-murakami]

Related to #2543

Implements health checks and logging for MySQL container and updates GitHub Actions workflows to ensure E2E tests pass without MySQL container issues.

• MySQL Container Configuration: Adds a health check to the MySQL service in compose.yml to ensure it's fully operational before proceeding with tests. Also, updates logging options to capture more detailed information for debugging purposes.
• Playwright Test Configuration: Introduces a pre-test hook in playwright.config.ts to check the health of the MySQL container and ensure connectivity. Adjusts the webServer configuration to wait for the MySQL container to be fully operational before starting tests.
• GitHub Actions Workflows: Updates the workflows for admin, selfhost, and visitor tests (playwright_admin.yml, playwright_selfhost.yml, playwright_visitor.yml) to include a step for logging the status of the MySQL container before running tests. This step aims to provide insights into the MySQL container's state, aiding in troubleshooting and ensuring test reliability.

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[ryota-murakami]

Add logging for MySQL container status and improve container health checks.

• Introduces logging commands in GitHub Actions workflows (playwright_admin.yml, playwright_selfhost.yml, playwright_visitor.yml) to log the MySQL container status, enhancing debugging capabilities.
• Implements a health check for the MySQL container in compose.yml, ensuring the container is ready before proceeding with tests.
• Adjusts logging settings for the MySQL container to limit log file size and number, preventing excessive disk usage.
• Adds a custom event listener in playwright.config.ts to log when the MySQL container is ready, improving feedback during test execution.

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For more details, open the Copilot Workspace session.