The solution to this is to create my own Custom query and subscription instead of the generated ones, and only include the ones I want in the payload.
The generated query and subscription have ~2.9k lines of code, and with hours of testing in AppSync console, I discovered that it probably exceeded the payload size (240KB over WebSockets and 120KB MQTT over WebSockets).
It is not too friendly that not even an error is thrown when the accumulated payload size is exceeded.
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