I found this article. Same idea applies I assume
https://blog.railway.com/p/postgre-backup

Hey, there is no native volume backup for Hobby plan users. You will have to backup your database yourself using pg_dump or utilize a Railway template that does it periodically by uploading the dump to an S3 bucket. You can then restore your latest backup using pg_restore. Just look up Postgres Backup or Postgres S3 when deploying a template and you should be able to find one that will suit your needs.