What is the best way to get an API token from a Connect app?

Hi, I need to build a Connect App that will allow users to make screen recordings directly from their browser and add a link to that recording into Jira Service Management Requests.
The resulting video has to be processed by our backend service before beeing posted a few time later into the conversation flow: What would be the best way to get an API token from a new installation of our Jira app, in order to allow our backend to post Request comments?

Note: sadly Forge and Web-triggers can’t be used because Forge apps cannot display (yet) into the customers Request Forms…