Make as much of the app static as possible. Run as much of the logic in the browser as possible.

Once you've isolated the "must be on the server" stuff, put an intelligent rate limit on it, add auto-scaling with upper limits, and prepare a page to be shown when the server goes down.

Highly dependent on your stack but there are plenty of free tiers for most serverless services. E.g. if you're willing to write everything in JS/TS then Vercel is a great option. (Kind of relevant to your post about adapting architecture to cost)