One possible approach to practice is skipping the “solutionizing” part of the listening-paraphrasing-solutionizing habit you mention. A good listener is able to understand the speaker and prioritizes understanding the speaker’s ideas over conveying their own.
Generally a good way to stay engaged is staying curious in what the other person is trying to communicate. Most people enjoy talking about their lives and will enjoy dominating the conversation. However if you need to fill a silence, a good personal story relating your experience to theirs is an effective way to demonstrate that 1) you’ve been listening diligently and 2) they’re not alone. Always nice to promote a sense of human togetherness!