Some friendly guy on the Godot discord(@xill47) suggested to use Microsoft.Data.Sqlite instead of System.Data.SQLite. Which worked 
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Also, little bit later I decided to have my db encrypted with password, for that I switched to the sqlite-net-sqlcipher (GitHub - praeclarum/sqlite-net: Simple, powerful, cross-platform SQLite client and ORM for .NET) which works nicely too.
I create an encrypted db like so:
SQLiteConnectionString connectionStr = new(DBPath, true, password);
DB = new SQLiteConnection(connectionStr);