Hi,
So you mean that when you click on the radio button for the PayPal payment method it works fine. However, when you then click on the "finish" button, you get the whirling icon and it then redisplays the checkout page without any error message.
What if you disable the Braintree payment method ? Do you still have the issue with the PayPal payment method ?
If yes, then I don't know what it could be. I've never seen the PayPal plugin refusing the checkout completion anywhere. Maybe a custom plugin acting strange could be the reason ?
If no, then I suppose that it's linked to the Braintree payment plugin not accepting the order creation because its credit card form is not filled in even though it isn't selected as payment method, or something like that and so in that case, you'll probably have to check with the developer of the Braintree plugin.