We use Google cloud run for this. They bill per request and you can run whatever docker container you want. I currently have a small setup with two separate kotlin based server applications running there (one based on spring boot and one on ktor). We use firestore as a cheap datbase (billed per read & write). Both have a free tier. So it's costing us next to nothing currently because neither docker container is getting a lot of traffic. Basically the bill for last month was only around 2$ for one of these applications (the other one I only deployed a few days ago).

Basically, at some point it gets expensive of course but when you are simply testing out stuff and don't expect a lot of users to show up, it's actually not bad.