Hey there, JiriHc.
After reviewing your post, it appears that you're having a problem sending payments through the Messages application on your 2020 iPhone SE. You receive a message that it wasn't delivered, and we're glad to help with this.
If you can't send or receive messages on your iPhone, iPad, or iPod touch -- Apply the steps under "Try these steps first", then select "Message not delivered" just below. If you’re able to send SMS messages other than sending money, continue below.
Set up Apple Cash -- Make sure that Apple Cash has been set up correctly. Start with the steps under "What you need", then proceed through the rest of this article.
Send and receive money with Apple Pay -- From the screenshot you provided, it appears that you understand the steps. Sending this article for you to review.
Let us know how that goes.
Take care.