How do you manage people who don't necessarily report to you? This could be while giving feedback on a piece of work? Or getting them to prioritize the project you're running.

My suggestion is to reframe your thinking from "managing people" to collaborating with people who don't report to you. As leaders, we should manage processes and not people. The simplest way to work with others, both those who may or may not report directly to you, is to build strong relationships built on respect and communication. Fostering collaboration is key by first ensuring you're aligned on the project's goals, then be sure to include them in the decision making process, or acknowledging their contributions to the work.