I've been using Google App Engine as the backend of my scratch-my-own-itch Android app. Granted it only has 60+ active users (according to Google Play Console) but my monthly bill for that has always been <$1 (the parts that's not free are secret manager and storage to store my deploys).

You can even run multiple App Engine apps for mostly free, because their free tier is calculated based on the actual instance-hours running, and with App Engine you can configure it to that when you don't get any traffic there's no instance running (they spin up a new one when there's a new request in that case).