Gmail sync problems on iOS or iPadOS are slightly different. There are some troubleshooting steps that are similar to those for Android, but a few fixes are specific to Apple devices.
1. Check your IMAP is enabled
2. Make sure the device is online
3. Restart your iPhone.
4. Check your push settings
5. Reinstall the Gmail App
6. Delete your account
7. Check if the app needs an update
See also - https://emailspedia.hpage.com/why-is-gmail-not-syncing-on-iphone.html