Repeating back what someone said (specifically: trying to mirror their exact words as best you can remember them) also has proven psychological effects: increased empathy and calming of your own emotional response and theirs.

It's a component of a few psych frameworks around improving interpersonal conflict. Ref: https://hartsteinpsychological.com/the-power-of-active-liste...

Short template form is "What I think I heard you say is (repeat their words as exactly as possible)? Did I get that right?"

Yeah, 100% agree with that.