After not really paying attention to my flight records for a couple of months, I tried to sync all of my flights and am missing all the flights from June and July. Am I correct in assuming that all flights are automatically stored on DJI servers?

No flight records are not stored automatically unless you sync your flights manualy via the dji go app.
Flight records are stored via cloud which updates your dji go account so flight distance wont be correct unless you update/sync your flight records regularly preferably after each flight.

Hello there. Thanks for reaching out DJI Forum. However, flight records are not stored automatically. You you'll need to sync your flights manually using DJI go 4 app or using DJI Assistant 2. For reference, you can watch the video tutorial below. If you have other concern, please let us know. Thank you.