Navigate to the Account Selection > Select your casino account that's under the 403 error and click on "Settings"
Select a different mirror than "stake.com" or your current mirror (e.g. stake1021.com)
Get your API key from this mirror and paste it in the app
Click on "Casino Website" in the top right corner and wait until you see the home page of Stake/Primedice. You do not need to log in in this window! If that doesn't work, set the Cloudfare cookie manually
Close the pop-up window of the Stake/Primedice website
Click on the green "Connect" button and you're set