I deployed and published my app to the Google Play Console 6 days ago and the status is stuck on "internal testing". Do I need to do something? Or how much time does it take to publish the app?
It seems like you have published your app on the Internal Testing Track instead of the Production track. That is why it is not published.
To publish it on the Release track go to "Release" > "Production" > "Releases" > "Create new Release". Now add your apk/app bundle and publish it. It should get reviewed and published within a few days.