For some datasets' dataverse_json exports, the `citationDate` key and the `citation` key contain the wrong dates

What steps does it take to reproduce the issue?

• When does this issue occur?
  When looking at the dataverse_json exports of some datasets

• Which page(s) does it occurs on?
  In the dataverse_json exports of some datasets, but not all datasets

• What happens?
  In the dataverse_json exports of some datasets, the citationDate key and the citation key are not showing the date of the date field that was used with the API endpoint for changing citation dates. It's showing a different date, possibly the dataset's Publication Date (when the dataset was first published in the Dataverse repository).

  For example, see the dataverse_json export of the dataset at https://doi.org/10.7910/DVN/5KLDV6, whose citation date was changed to be the same as the dataset's Distribution Date (which is 2025-11-14 and is used for the year in the dataset page's blue suggested citation box).

  In the dataset's dataverse_json export, the date in the citationDate key is not the date that's in the dataset's Distribution Date field. It's the same date as the dataset's Publication Date.
  

  And the year in the citation key is not the year that's in the dataset's Distribution Date field.
  

• To whom does it occur (all users, curators, superusers)?
  All users, curators, superusers

• What did you expect to happen?
  When users use the API endpoint for changing a dataset's citation date, the date in the citationDate key and the year in the citation key should be the date and year of the date field that the user used in the API call, such as the Distribution Date.

  This bug makes it harder for users to use the Dataverse API to get certain information about datasets, such as for reporting about datasets in their collections. And it might affect the SPA/Modern, since we write in #9656 that we added the citationDate key to the dataverse_json export for the SPA/Modern.

Which version of Dataverse are you using?
v6.9 (on Harvard Dataverse) and v. 6.10 bugfixes (on Demo Dataverse)

Any related open or closed issues to this bug report?

• https://github.com/IQSS/dataverse/issues/9656
• https://github.com/IQSS/dataverse/issues/12315

Reproduce the problem with the linked dataverse_json export and the API endpoint for changing citation dates, comparing citationDate and citation with the selected date field. Trace the endpoint and dataverse_json export path, then compare the behavior with related issues #9656 and #12315. Done means both exported values use the date selected through the API.