BibTex citation export needs support for @dataset and eprint fields (and other improvements)

Overview of the Feature Request
As reported before by @adam3smith, our current BibTex export is somewhat flawed. While trying to be as close to the orignal BibTex specification as possible,

• it uses a custom (invalid) type "@data"
• it adds a non-existing (custom) field "UNF" for file citations
• it uses an "url" field, which is only specified by BibLaTex
• it uses "booktitle" as a field for the dataset name when it's a file citation
• it doesn't make use of modern BibLaTex fields like "eprint" or "related".

We should modernize the BibTex Export. If necessary, it should be renamed to "BibLaTex" to better indicate the necessary usage of it. Any of the above entry types and fields are included in BibLaTex 3.13+ (released 08/2019). The ecosystem has moved on, so should we.

We may still keep the original exporter around, but make it opt-in. In case people report complaints, they can re-enable it in their installations.

For more details on BibLaTex, here's the documentation for the package: https://tex.org.uk/macros/latex/contrib/biblatex/doc/biblatex.pdf

What kind of user is the feature intended for?
(API) User, Guest, ...

What inspired the request?
Working on #11892 and moving citation generators into the exporters framework.

What existing behavior do you want changed?
The current BibTex export needs an overhaul.

Any brand new behavior do you want to add to Dataverse?
None.

Any open or closed issues related to this feature request?

• #6613
• #3759

Are you thinking about creating a pull request for this feature?
Help is always welcome, is this feature something you or your organization plan to implement?

Start by locating the current BibTeX exporter and reviewing related issues #6613 and #3759, then compare its behavior with the BibLaTeX 3.13+ documentation linked in the issue. Done means the project has an agreed export design covering @dataset, eprint, related, and the listed legacy fields, including whether the original exporter remains opt-in.