How do I change a monthly billed storage plan to annual billing?

You cannot. There are no annual plans. They were discontinued. There are only monthly subscriptions now.

The only people with annual plans now are those who already subscribed for one prior to their discontinuation in 2015 and chose not to then upgrade to a monthly plan. But since 09/2015 there has been no option to move to an annual plan.

Annual iCloud storage plans - https://support.apple.com/HT201058 - "We introduced monthly storage plans and pricing on September 16, 2015." ... "If you don't switch to a monthly plan, your annual plan continues to renew on your original purchase date." I.e., you used to be able to pay annually but if you stopped you can't now. Presumably you cannot now change to an annual payment plan either. If you do not want to add a credit card to your payment information you can use a gift card to make sure your iTunes Store balance has enough money to cover long-term deductions.

That's what my post told you (except I presumed you would read what Apple actually said about the non-availability of annual plans in the link -- but I am quickly discovering I have to copy entire secions out of links and paste them here so people only have to read the pertinent bits since increasingly nobody is bothering to read links). Plus it told you a way to avoid having to do it EVERY month!!!!