QGis snapping configuration is applied to the active layer. In this way, if we want to set different configurations (in that case : overlap) to different layers, it is not possible.

In our case :

A good way of solving it would be to add a toggle for overlap on the digitalisation settings, exactly like it is done for the snapping (cf. the picture linked). This solutions was proposed by nirvn here : https://github.com/opengisch/QField/issues/6410