I've been using YNAB4 for the last few years, and I like it so much that I haven't switched to the web version (new YNAB) yet. However, I have played around with the web version a little, and here is what I have discovered.
Despite the different look of the credit card account and the lengthy dissertation on the credit card differences in the Transition Guide, credit cards are handled almost exactly the same in the new YNAB as they were in YNAB4.
You enter credit card spending transactions in the same way as YNAB4. When you enter a transaction, money is pulled out of the budget category you select. The only difference is that in YNAB4, this money was considered "gone." Now, that money moves from your budget category into the new credit card category.
When it comes time to pay the credit card bill, you also enter this transaction in the same way as before. It is entered as a transfer of money from your checking account to your credit card account. The only difference here is that with new YNAB, the funds are deducted from your credit card category. This is handled automatically, so you don't have to think about it if you don't want to.
If you always pay your credit card bill in full, you never have to budget money manually into the credit card category. The money will already be there from when you entered the credit card spending transactions. The only time you would manually budget money into the credit card spending category is if you have old credit card debt that you are trying to pay off.
A quick example, in pictures:
I start out with $10,000 in my checking account, and no credit card debt:
I've got all $10,000 in my "Fun Money" category:
Now, I spend $100 at the Store:
You can see that, just like in YNAB4, the credit card account is now in the red $100, and the checking account balance has not changed.
In the categories, my Fun Money category is down $100 to $9,900, just like it would be in YNAB4. The only difference is that there is now $100 in the new Credit Card Payments category.
When it is time to pay the bill, I enter an account transfer, just like in YNAB4:
Note that the Credit Card balance is back to $0, and the Checking Account balance is now down to $9,900.
The Credit Card Payment budget category is now magically back to $0:
The above example starts with a zero balance on the credit card. However, most people will have a non-zero balance on their credit card when they first start a budget. In YNAB4, when you added a credit card with a (negative) balance, the debt was shown in a budget category called "Pre-YNAB Debt." You then added money to this budget category until it went to zero, and then you didn't need this budget category anymore.
With new YNAB, credit card balances are not shown in budget categories. If you add a credit card account with a balance, the debt is not shown in the budget categories. To pay off this debt, you can fund the Credit Card Payments category. After this existing balance amount is paid off, you won't need to fund the Credit Card Payments category anymore as long as you properly assign each new credit card purchase to a funded budget category.