database.sql is the file where the plugin is going to store the database.
If you have a lot of records, it can be quite large. Some plugins log login attempts and activity. This creates a lot of data in the database and I’ve seen databases grow to 10-20GB of size just from these records. So you can really be going out of disk space.
The other possible issue here is that there is a limit on the maximum file size that you can create on the disk. Some shared hosting providers limit this to 2GB, some to 4GB, and some to 8GB.
So when the database is being saved it reaches 2GB or whatever the limit is and then the filesystem does not allow the plugin to write any more data mimicking not enough disk space.
Ask your hosting provider what is the maximum file size that you can create. Then ask them for error logs from apache/nginx/php and review the logs for issues around the time when you attempted to export your site.