Beginning of an answer, I will do it better soon.

Based on my understanding, you have Atlas layer that contain polygon. Some are made to be set the view on a regional scale and some are made to get a view at a local scale. These polygons can cross one another.

In your example, you want to show a label that is in your map view, but that doesn't cross other polygons existing in your atlas layer.

The solution would be to set your atlas layer to not render the current polygon used for atlas. You will get the same result as you show in your screenshot. Then you set the label in your atlas layer to be blocking. Only the feature not used as atlas will block the label to be created.

A problem will still exist for your city map as the polygon for regional map will be visible and will block your label. Can you share attribute table for some features ?

Based on my understanding, you have Atlas layer that contain polygon. Some are made to be set the view on a regional scale and some are made to get a view at a local scale. These polygons can cross one another.

In your example, you want to show a label that is in your map view, but that doesn't cross other polygons existing in your atlas layer.

The solution would be to set your atlas layer to not render the current polygon used for atlas. You will get the same result as you show in your screenshot. Then you set the label in your atlas layer to be blocking. Only the feature not used as atlas will block the label to be created.

The problem will still exist for your city map atlas feature as the polygon for regional map will be also visible and will block your label. To solve this, you could add a rule of visibility based on scale to have no atlas feature shown at the smallest scale.