If we are talking about 3rd party tools, you can use the Skyvia connector for Airtable and MySQL integration

Skyvia offers a cloud data integration platform that allows for easy connection between BigQuery and Airtable without the need for coding. This platform operates on a freemium model, providing users with a range of features at no initial cost.

I used Jitterbit for integration. Works correctly

I used Skyvia for integration. Works correctly

You can use the Skyvia Backup service for backup, including automatic backup.