Is it permissible for imams to recite verses that are appropriate for prevailing circumstances, such as rainfall, death, or what is being discussed in a sermon before or after prayer? And is this considered an innovation (bid'ah)? And what is the criterion for innovation in this case?

It has not been authentically reported from the Prophet, peace and blessings be upon him, that he recited specific verses when rain fell or when someone died. Doing so is not considered an innovation (bid'ah) unless one consistently adheres to it or believes it to be a Sunnah (definition). Indeed, the consistent recitation of specific verses at specific times or on specific occasions, with the intention of it being a Sunnah, without evidence, is considered an innovation, and "whoever performs an act that is not in accordance with our matter, it will be rejected."