Is there any evidence that the Imam seeks refuge [with Allah] upon forgetting or making a mistake in recitation during prayer, especially in Tarawih prayers?

We do not know of any specific evidence for seeking refuge from Satan when forgetting something from the Quran, neither from the Prophet (peace be upon him) nor from the Salaf. However, if Satan afflicts the worshiper during prayer and confuses their recitation, then it is permissible for them to seek refuge with Allah from him, as stated in the hadith of Uthman ibn Abi al-Aas and the hadith of Abu al-Dardaa concerning repelling Satan who afflicts the worshiper. It is recommended to seek refuge along with spitting to the left three times. If the recitation becomes confused for the worshiper, or if they are prompted but do not grasp it, they may seek refuge. The seeking of refuge should be in the first rak'ah of the prayer, unless something occurs that necessitates seeking refuge, such as excessive whispers. As for seeking refuge merely for habitual error or forgetfulness, it is not prescribed.