By default, Burp Suite is able to intercept the request from the page, but not getting the JSON response. What rule should be added in the 'Intercept server responses' menu (in the 'Proxy > Options' tab) to be able to edit the JSON responses received from the server.
BurpSuite will not intercept server responses by default and display them to you.
To enable this functionality go to:
Proxy -> Options -> Intercept Server Responses
And make sure to check the box next to
Intercept responses based on the following rules
Then either select one of the displayed rules or add one like the highlighted one below:
Also make sure to enable Intercept in the Intecept-tab.