Flying into USA via Europe/Singapore on Advance Parole (AP)?

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I am seeking clarification on the use of Advance Parole (AP) for re-entry into the United States after international travel. Specifically, I am planning to return to the US from India with a layover in either Europe or Singapore. This will be my first time using Advance Parole. I possess an H1B visa stamp in my passport valid until 2026, but I am no longer employed by the sponsoring employer. Although I recently traveled from the US to India with a layover in London, I understand that regulations regarding AP travel may differ for departures and returns. Additionally, I am exploring cost-effective travel options and have observed that Middle Eastern airlines are generally more expensive than European carriers. Thank you for your time and expertise.

Thanks.