Handle.net PIDs - Styled Citation shows "doi" instead of "hdl"

What steps does it take to reproduce the issue?

• When does this issue occur?
  Be clicking on filed "Cite Datasets -> Show Styled Citation"

• Which page(s) does it occurs on?
  dataset main page

• What happens?
  In the field "Cite Datasets -> Show Styled Citation" as PID is written "doi", however Handle.net provider is used - so "hdl" must be shown. The same happens for styles, where complete URL is provided instead of doi/hdl - the URL is created based on doi style, https://doi.org/handle-prefix/handle-shoulder/PID - so, fully wrong URL as a result.

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

• What did you expect to happen?
  Different full URLs and short references for DOIs and Handles.

Which version of Dataverse are you using?
6.10.1

Any related open or closed issues to this bug report?
https://github.com/IQSS/dataverse/issues/12244

Screenshots:

Start at the dataset main page's “Cite Datasets → Show Styled Citation” entry point and compare the behavior with related issue #12244. Verify that styled citations use provider-specific PID labels and URLs, with distinct results for DOI and Handle.net identifiers.