As shown on SQLite's page Appropriate Uses For SQLite, a client/server database like MySQL would work better for client/server applications, high-volume websites, very large datasets, or high concurrency. Nothing of this applies to your offline application, so you should use a database that was designed to be embedded (not necessarily SQLite).
MySQL has an embedded server library which can be linked directly into an application. When using C#, the MySQL library is linked into the .NET MySQL database driver, so using the embedded server would require recompiling this driver. And such linking will trigger MySQL's GPL license. And:
The libmysqld
embedded server library is deprecated as of MySQL 5.7.17 and will be removed in MySQL 8.0.
It would be possible to install the standalone MySQL server yourself; this is described in Installing MySQL on Microsoft Windows Using a noinstall Zip Archive.
However, this would still run the MySQL server as a separate process or service, and this could conflict with other installations on the machine; it would be your installer's responsibility to configure that MySQL instance correctly for whatever environment it encounters on the target machine.
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