HTTP 503 is a temporary error code (“Service unavailable”) indicating iCloud servers aren't responding correctly to requests from your devices. The error typically gets resolved as Goodnotes automatically retries, but if the error somehow lingers on, sync failures might result.
This issue is not apparent to us and we know of other apps experiencing the same issue. [1]
For now, please try these suggestions.
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References:
[1]:
https://developer.apple.com/forums/thread/695278
https://developer.apple.com/forums/thread/695050
https://developer.apple.com/forums/thread/694496
https://www.macrumors.com/2022/01/24/developers-icloud-unreliability-bug/