Custom field type object with sub properties of searchType date

I’ve tried to add a custom field type with roughly this schema:

modules:
  jira:customFieldType:
    - key: ft-test
      name: Testing
      description: ...
      icon: https://developer.atlassian.com/platform/forge/images/icons/issue-countries-icon.svg
      type: object
      formatter:
        expression: |-
          let sent = typeof value.sent != "undefined" && typeof value.when != "undefined" ? 'Sent ': '';
          `${sent} ${value.when}`
      schema:
        properties:
          when:
            type: string
            searchType: date
            searchAlias: When
          sent:
            type: string
            searchType: date
            searchAlias: Sent
      # ...

The values I store into the custom field look like this: { "when": "2022-10-06T11:33Z", "sent": "2022-10-06T11:33Z" } or { "when": "2022-10-06T11:33Z" }

When I try to search for the properties of custom fields with this type with JQL I never get any results.
Example JQL, this should always return something (x > now() OR x < now()) but the result is empty:

"issue.internalProperty[ft-test__fc581629-a5d9-4212-a1cd-e0b7e8ea561d].when" > now() OR
"issue.internalProperty[ft-test__fc581629-a5d9-4212-a1cd-e0b7e8ea561d].when" <= now() 

Is the date format that’s stored to the fields incorrect? Are there any other workarounds?
(one workaround I could think of is using type: number and storing unix epoch seconds)