Can a private nonprofit entity that wants to submit a project for instance on circular economy be concerned by de minimis?

The de minimis declaration has to be seen in the context of the risk of state aid relevance. If the risk of state aid relevancy is confirmed and the risk cannot be removed, the Programme may grant Interreg funds under the de minimis regime for partners receiving external public co-financing to their budget (including SMEs). Please check out the Programme manual for details on state aid relevance and the possibility that the Programme may grant Interreg funds under the de minimis regime.
The question of State aid is not linked to the nature of the partner organisation, but to the nature of the activities.