The Issue and Task data is accessible from the API (both REST and Query) the same way as other record data. In order to interact with Issues and Tasks via the API, you will first need to get the Form ID for each one.
Make a Get Request to get the Form ID
In order to obtain the Form ID for either Tasks or Issues, utilize Get All Forms and set the type to "system".
The response will include 2 forms: "Issue" and "Task Creation". You can search and copy the
"form_id" value for each one that you are looking to interact with. One thing to note is that the search will display 3
"form_id" values. You will notice that two of the values are the same (the Tasks' form id).
Here is a sample response where you can locate the