You do not need a Coinbase account to deposit with a debit card or with Apple Pay.
Both work on their own in the mobile app: tap Debit on the Deposit screen, and the Deposit cash screen offers Apple Pay where it is available to your account, or your debit card under Details.
A Coinbase account only comes into play if you choose Exchanges and apps on the Deposit screen, where Coinbase is listed when it is available to your account. That option lets you fund from your Coinbase balance, so it needs an account. Every other method works without one.
If you pay using the Apple Pay method and see a payment provider's name on your bank statement instead of fomo's, that is normal. That provider handled the payment, and it does not mean an account was created with them.
Depending on your account, the Apple Pay method may have a weekly spending limit and a cap on how many transactions you can make in total.
Open Details on the Deposit cash screen and the row next to Payment method shows your weekly figure. When you reach a limit the screen says so, and where an increase is available the button reads Increase limit.
You can also pick Debit card under Details on the Deposit cash screen, use Coinbase under Exchanges and apps if you have an account and it is listed for you, or deposit USDC directly from another wallet or exchange.