The hobby plan is a $5 monthly subscription for the account, and it comes with $5 in credits every month that are used towards your resource usage (they do not roll over).

On average a MySQL database will cost about $5 a month to run, your included credits will cover that, but would not cover the NextJs app.

You would for sure end up paying more than $5, not all that much more, but it would be more.

To lessen costs, look into using the MariaDB template, it should be a drop-in replacement for MySql, and it uses less idle memory in my experience, though I make no promises that this would bring your costs within the included usage, but it would bring it closer.