By using async it's converted into asynchronous action and being send to the queue in the background

Nope. It does not run in the background. It's not even deferred to "later", the function body starts executing immediately. The only difference that it can await something, at which point the async function returns a promise for its eventual result, after the "something" has finished. But Vue ignores that returned promise (like any return value).

So yes, code after the await might run "out of order", after another hook like mounted was called, but it'll still run in the foreground at that point. In other words, if mounted relies on some stuff from created, that will need to be done synchronously. You can still do that in the first part of an async function though.

This is not any different from creating a promise chain in a created method that is defined without async.