I don’t see any reason why you couldn’t host Sentry yourself on Aptible but, as always, I recommend reviewing the Is my application a good fit for Aptible? topic to check for common pitfalls.
As described in this topic Aptible used to provide base images but that was before many official images were available. Now we recommend using official images or those provided by the service you want to integrate with.
There is an official sentry image but it appears it was deprecated about three years ago in favor of getsentry/sentry. Using this image as a base and the instructions from the Sentry Self Hosted doc to configure the application should be sufficient to get it running. It looks like the docs they provide assume you’re manually building and deploying from the provided repository using docker-compose so keep that in mind when reading through it.