The new Incident ticket needs to be generated based on "HPD:IncidentInterface_Create", rather than "HPD:Help Desk" form.
Need to configure Rest API correctly on AR Server side and grant tokens for the login account. Please consult the article linked below.

Using POST action to generate a new entry based on "HPD:IncidentInterface_Create" form through the link:
http/https://<servername>:<port>/api/arsys/v1/entry/HPD:IncidentInterface_Create/

Note: In order to fetch response such as Request ID or some other field ID, use below format:
http/https://<servername>:<port>/api/arsys/v1/entry/HPD:IncidentInterface_Create?fields=values(Request ID, Incident Number, Urgency, Priority)

Headers:
Content-Type: application/json
Authorization:AR-JWT {{jwt}} 
where jwt is the token generated for the login account beforehand.       
        Note:  if using Oauth2 authentication, use these headers instead>
         Authorization:  Bearer {{token}}
         X-Requested-By:  XMLHttpRequest 

The following fields are required to be included in your request at the body tab in raw format: For example

Create Incident using rest (without assignment of the case while creating)

{
    "values":
        {

        "Description":"Test111",
        "Urgency":"4-Low",
        "Impact":"4-Minor/Localized",
        "Company":"Calbro Services",
        "Assigned Group":"Service Desk",
        "Status":"New",
        "Reported Source":"Direct Input",
        "First_Name":"App",
        "Last_Name":"Admin",
        "Service_Type":"User Service Restoration"

        }
}

Created a ticket and assign it to a specific group via rest
e.g
{
 
  "values":
    {
    "Description": "REST API: Incident Creation",
    "Urgency":"4-Low",
    "Impact":"4-Minor/Localized",
    "Company":"Calbro Services",
    "Assigned Group":"Backoffice Support",
    "Assigned Group ID" : "SGP000000000009",
    "Assigned Support Organization": "IT Support",
    "Assigned Support Company":"Calbro Services",
    "Status":"New",
    "Reported Source":"Direct Input",
    "First_Name":"Allen",
    "Last_Name":"Allbrook",
    "Assignee":"Mary Mann",
    "Service_Type":"User Service Restoration",
    "z1D_Action":"CREATE"
    }
}

You need to replace the values above with the proper value in your environment.
If there is any error in return, please enable ARfilter log and reproduce the error for troubleshooting.

Check this article to know more about REST API:
AR Server REST API architecture and overview - Start here

https://docs.bmc.com/docs/itsm2002/the-rest-api-references-976798064.html
https://docs.bmc.com/docs/ars1908/calling-third-party-rest-apis-in-a-remedy-application-881403083.html
https://docs.bmc.com/docs/itsm2002/integrating-itsm-with-third-party-applications-by-using-the-rest-api-932206743.html