Background: I started at a large, multi-national corporation in the United States about a half a year ago. My intended position was as a mentee in a very specialized area for the next two years, before becoming a senior designer. Due to some interesting circumstances and some skills I brought to the team outside of my experience, I am now the senior advisor on the system I was meant to be mentored on, as well as owning significant portions of other subsystems in other design areas. Recently, I have been made the team POC (point of contact) for internal and external PRs (problem reports).
Current Situation: At the beginning of last week, a conversation was occurring around my work area I was not tuned into. At a certain point, I heard my team lead loudly ask "you heard that, agentroadkill?" I was then told I would be taking over as POC for the largest current project, which is very important, visible, and objectively, not going great (outdated design and rushed schedule are almost entirely to blame). I was told other teams and the customer would be instructed to come to me with design PRs and questions, and that I should "babysit" the other design assets tasked to the project. I am taking over from a coworker who has worked there for 4+ years, and has more experience in certain problem areas than I do. I understand my job is not so much managerial as executive: I don't task resources or make decisions, I essentially route information internally and externally, and provide support when needed.
Question: The colleagues on my team now more-or-less look to me for guidance about which task they should be working on next (one of them is asked about specifically here). I have no real power over them, and some are reluctant to comply with my attempts to organize the chaos surrounding the project (I work on the project as well, so I understand the frustration with new process and overhead, but the outside-facing stuff is simply not possible without some process and better documentation). What are some effective strategies to manage people who are my colleagues, not subordinates? It is worth bearing in mind I am the second-newest member to the team, and the youngest by (I estimate) 4-5 years.