Hey Nathan,
You need to use the PowerBI Service web site to add new fields:
- Open your PowerBI report in the PowerBI service ( https://app.powerbi.com )
- Click the edit button
- Click your Power Apps for PowerBI visual
- Change the columns (add/remove columns)
- Note: After adding the column, you may also have to click the dropdown by the column name and choose "show items with no data"

- Note 2: You can validate that the visual is receiving your data by clicking the 3 dots > show as table
- If you see blanks, like the screenshot below, then go back to the report and choose "show items with no data"

- Note 3: if you've selected "show items with no data" for every column and it still isn't working, then you may have a column that doesn't have data, put that column last (my ISSUE_URL doesn't always have data, so I put that last in the column list).

- Once you know it is working in powerbi, click the dropdown and then "Edit" (remember, this is all happening in your web browser). It should open your powerapp. I usually make a minor change, save, then publish
It is pretty finicky, especially the part about the blank fields. When in doubt, start simple and then add fields from there.
Another thing to watch out for: when setting up the initial connection from PowerBI to Power Apps: If you select "Create New App", the PowerBIIntegration object in your Power App will have a "Refresh()" method that supposedely lets you tell powerbi to refresh the page from within powerapps.
If you instead create the Power Apps app first (in power apps), and then when adding the "Power App for PowerBI" visual (from PowerBI) and select "choose existing app" from Power BI, you will not have the "Refresh()" method.
This may not matter for your use cases, but for mine, I ended up having to let PowerBI create a brand new power app and then I manually rebuilt it so I could gain the .Refresh() functionality.
Good luck!
--
Nathan