Is vocalizing the intention a Bid'ah (innovation) and misguidance that leads to the Hellfire?

Innovation and introducing new practices in religion are sins for which the doer's عمل (deed) is rejected and not accepted, and Allah threatens the perpetrator with Hellfire. However, there are impediments that may prevent this threat from materializing, such as: if the person has good deeds that outweigh their bad deeds, or if they perform good deeds that efface their bad deeds, or if intercessors intercede for them, or if Allah forgives them, or if they have an excuse like ignorance or following a reputable scholar. It has not been authentically reported from the Prophet (peace be upon him) and his companions that they vocalized the intention. The prescribed method is to internalize it in the heart, and vocalizing it is a rejected innovation for which no reward is granted. However, the doer does not incur sin unless they know of its innovated nature and insist upon it without a permissible interpretation or following (a scholar). Increasing the supplication is not an innovation as long as the supplicant mentions it as a form of supplication and does not attribute it to the Prophet (peace be upon him), though adhering to the established wording of remembrance is preferable.