I am an idiot. The log statement was converting the result to a string which truncates the metadata that comes with it and only returns the array of results, of which there are none. I am able to access the result directly via

...
const insertResult = await connection.query('INSERT INTO MY_TABLE VALUES(1, \'Name\')');
console.log(insertResult.count);
...

Apologies for the misunderstanding but sometimes talking out the problem with a text editor is helpful :)