feat(cloudsqlpg): run SELECT 1 after successful connection attempt

[srividyareddy786]

Description

Should include a concise description of the changes (bug or feature), it's
impact, along with a summary of the solution

Update the initialization logic to execute a "SELECT 1" statement immediately after a successful ping. This confirms that the database engine is not only reachable but also ready to parse and execute SQL commands.

PR Checklist

Thank you for opening a Pull Request! Before submitting your PR, there are a
few things you can do to make sure it goes smoothly:

• Make sure you reviewed
  CONTRIBUTING.md
• Make sure to open an issue as a
  bug/issue
  before writing your code! That way we can discuss the change, evaluate
  designs, and agree on the general idea
• Ensure the tests and linter pass
• Code coverage does not decrease (if any source code was changed)
• Appropriate docs were updated (if necessary)
• Make sure to add ! if this involve a breaking change

🛠️ Fixes #2996

[gemini-code-assist]

Code Review

This pull request enhances the initialization of the Cloud SQL PostgreSQL source by adding a SELECT 1 health check and ensuring the connection pool is properly closed upon failure of either the initial ping or the health check. I have no feedback to provide.