Inconsistent JSON responses in Search and Native API for collections

What steps does it take to reproduce the issue?/ What happens?

1. Obtain the information of a single dataverse via curl "https://demo.dataverse.org/api/dataverses/root" | jq Response: [1]
2. Search for root dataverse via curl "https://demo.dataverse.org/api/search?type=dataverse&q=root" | jq Response: [2]
3. Compare the responses [1] and [2]. I expect the search response to be a subset of the details provided by the native API to obtain a single dataverse. However, "published_at" is only available via search. "alias" is called "identifier" within the search response, which is a bit confusing especially since there is a property "id" with the numerical database id of the dataverse.

[1]

{
  "status": "OK",
  "data": {
    "id": 2067773,
    "alias": "DVC_2023",
    "name": "Dataverse Community Meeting, 2023",
    "affiliation": "Harvard University",
    "dataverseContacts": [
      {
        "displayOrder": 0,
        "contactEmail": "sbarbosa@hmdc.harvard.edu"
      }
    ],
    "permissionRoot": true,
    "description": "This collection supports the Dataverse Community Meeting, 2023 training website.",
    "dataverseType": "TEACHING_COURSES",
    "ownerId": 1,
    "creationDate": "2023-06-05T07:40:29Z",
    "theme": {
      "id": 716,
      "logo": "NE_Revolution_Logos_Seal_Primary_RGB.jpg",
      "tagline": "I love football!!",
      "linkUrl": "https://www.boston.com/",
      "linkColor": "000d08",
      "textColor": "888888",
      "backgroundColor": "f7b100",
      "logoBackgroundColor": "08e7f7"
    }
  }
}

[2]

{
  "status": "OK",
  "data": {
    "q": "root",
    "total_count": 3,
    "start": 0,
    "spelling_alternatives": {},
    "items": [
      {
        "name": "Logo Bug Root",
        "type": "dataverse",
        "url": "https://demo.dataverse.org/dataverse/logobugroot",
        "identifier": "logobugroot",
        "published_at": "2021-11-23T11:30:06Z"
      },
      {
        "name": "Tania Schlatter Dataverse in Root",
        "type": "dataverse",
        "url": "https://demo.dataverse.org/dataverse/TSD_Root",
        "identifier": "TSD_Root",
        "published_at": "2021-11-16T11:37:10Z"
      },
      {
        "name": "Oscar Moreno Dataverse",
        "type": "dataverse",
        "url": "https://demo.dataverse.org/dataverse/root",
        "identifier": "root",
        "published_at": "2022-09-20T14:06:00Z"
      }
    ],
    "count_in_response": 3
  }
}

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

API users

What did you expect to happen?

1. Proposed change: include "published_at" within the detailed response.
2. Proposed change: renaming of "identifier" to "alias" to be consistent across API responses.
3. Proposed addition: In order to recreate the dataverse result cards within a SPA I want all the information needed tobe included within the the search response. Here the information like description, affiliation, parent dataverse, link to logo and information about the "linked" status are missing. Hence, I'd like those tobe included.
4. Proposed addition: Add parent dataverse and "linked" status to the detailed response.
5. Proposed change: Change value of logo in detailed response to be a URL, that can be used in HTML markup.

When does this issue occur?

Whenever I use the API.

Which page(s) does it occurs on?

API (see above)

Which version of Dataverse are you using?**

The latest

Any related open or closed issues to this bug report?

Start by comparing the native dataverse endpoint at /api/dataverses/root with the search endpoint at /api/search?type=dataverse&q=root using the supplied curl examples. Review the response contracts for naming, publication data, parent and linked status, and logo URLs; done means the agreed fields are consistent and sufficient for the requested API clients.