Is it considered an innovation (bid‘ah) to recite supplications (adhkar) that were not reported from the Prophet, peace and blessings be upon him, or to add specific supplications to legitimate ones, such as saying "A‘udhu Billahi minash-Shaytanir-Rajim" (I seek refuge in Allah from the accursed Satan) when pronouncing the Basmalah over food, or adding "SubhanAllah" (Glory be to Allah) once with it, provided that one does not believe in its superiority or habitually repeat it?

The most complete and best approach is to limit oneself to the specific ذكر (remembrance/invocation) mentioned in the Sacred Law. Adding to it is not an innovation (bid'ah) if its superiority or sunnah (definition) status is not believed in, and if it is not a continuous habit, but rather done occasionally. For the invocations transmitted from the Prophet (peace be upon him) are complete. The general rule regarding innovations differentiates between what is done occasionally and what is taken as a permanent habit. That which is permissible in its genus, but is taken as a permanent habit, becomes an innovation.