You can raise prices at any time without backlash, as long as current users continue to get the deal they signed up for. Just change it for new users.
The issue is then, if you raise prices too far, and fewer folks start signing up. You may want to lower prices, and update folks on the higher price to have the cheaper price (to avoid backlash).
With recurring billing you may see some users churn who "forgot" about the charge in the first place and were likely not using the product.
FWIW This past year ive been stung so much by SAAS price hikes its fundamentally changed my internal equation of "when to SAAS VS when to self-host/build". Messaging apps have been the worst offenders, adding new features that we don't use and using this as an excuse to up prices to ridiculous levels. Overall positive perhaps, now using more self-hosted OS software.