Is this act considered a Bid‘ah (innovation in religion): supplicating for a shoe to fall to the right if the action is correct, or to the left if it is wrong, in order to decide a perplexing matter?

This act has no basis in Islamic law, nor is it guided by reason. It is not permissible to perform it in a place of worship, like during supplication. Whoever believes in its permissibility has innovated, and whoever believes in its benefit has gone astray. It also involves a lapse in the etiquette of asking Allah the Almighty and falls under transgression in supplication. Allah the Almighty says: "Invoke your Lord with humility and in private. Indeed, He does not like aggressors." [Qur'an 7:55]. Furthermore, it resembles the pre-Islamic pagans in their practice of drawing omens.