What is the ruling on the prayer of a congregant who prays behind an imam who says a dhikr or du'a between the two salutations, and is his prayer valid? And how does he pray Jumu'ah if most imams do that?

The supplication between the two salutations is not prescribed. However, restricting oneself to the first salutation validates the prayer. Therefore, the Friday prayer and the obligatory prayers performed behind an Imam who supplicates between the two salutations are valid, although it is preferable to pray behind an Imam who does not engage in this supplication.