Hi @Crantz - thanks for the question. No worries, this is a very welcoming community. You will see that my app UX skill won't win design of the year award 😉
This is an interesting use case. You should we able to do all this within the Power App. Here's what I'd suggest:
1. Add the form processor control and then text inputs for each of the fields you want to display. Last, add a button.

2. For each of the text inputs, set each Default property to get the corresponding value to display what will get extracted by the AI Builder form processor control. To do this, write the following expression, using the name of the fields you defined on the AI model:

3. Test the app and upload a document. It should display the extracted values on the text inputs

4. Exit preview mode and now let's save the data to SharePoint. On the Data menu on the left, select Add Data and pick SharePoint.

5. Power Apps will then ask you to pick a list

6. Now on the button that we added to the app, on the OnSelect property set the following formula:
Collect('List name', {'Column name 1': TextInput1.Text , 'Column name 2': TextInput1_1.Text})
Replace List name, Column names to match yours, and add as many columns present on your SharePoint list

Now if you run the app and select that button, the data displayed on the text inputs should be saved to the SharePoint list. 🎉