Update specs for integrations API to check all modifiable fields

What does this MR do and why?

Previously only the event booleans were verified, but not any other attributes that were sent in the PUT request.

This is a step towards fixing inconsistencies in the Integrations API, some attributes are currently not supported and skipped in the specs.

This change also exposed a bug in the getters defined by data_field, where we'd incorrectly fallback to properties for falsy values. This should only be done for explicit nil values.

Issue: #348461 (closed)

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