The overall rule is that if all the software in your package is free open source GPL software, you can incorporate the community edition of MySQL, otherwise you need a commercial MySQL licence, see
https://www.mysql.com/about/legal/licensing/oem/
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My goal is to include everything that is needed to install the software such that the user does not need to configure anything.
MySQL has many versions running on many versions of many OSes with different amounts of RAM, varying load competition &c. Each instance relies upon a thousand or more configuration variables. So it isn't trivial to install.
And a non-trivial RDBMS instance is never static if it's successful i.e. used not dead,
so it needs to be managed by a DBA. Absent a designated DBA,
your user is the DBA.
So to be realistic, your no-user-configuration aim needs to become something more like ... designed for greatest possible ease of configuration with maximal support. Otherwise forums like this one wind up doing your tech support for you.