PHP Fatal error: Class 'Dfe\Stripe\Df\Payment\Method' not found in /var/www/public/app/code/Dfe/Stripe/Method.php

I have investigated your case.

1. Investigation:

1.1

First of all, I have noticed that the «Stripe» extension is not installed in your store despite I have installed it earlier:

1.2

I have tried to install it again using the official installation instruction
I have got a failure: «Authentication failed for code.dmitry-fedyuk.com».

Your store uses the login / password authentication for the Mage2.PRO code repository, but the credentials in the Composer’s auth.json file are wrong:

Solution:

Step 1

You should set the right credentials in the Composer’s auth.json file.
See also the «Authentication failed for code.dmitry-fedyuk.com» topic for more detailed explanation.
If you do not know your password for Mage2.PRO code repository, then you can restore it.

Step 2

Then you will be able to install the «Stripe» extension using the official installation instruction.