If you're looking to automatically extract Gmail emails (including replies) into MySQL and properly group conversations, this is exactly what my SaaS Sivox does.

Sivox connects to Gmail (and Zoho Mail), automatically fetches emails, extracts metadata (including thread and conversation grouping), attachments, and stores everything directly into MySQL or SQL Server databases.

You don’t need to deal with APIs, IMAP or complex scripting — everything is fully automated and works continuously.

You can check it out here is free:
👉 https://sivox.net/

Happy to give you more details if you're interested.