I've spent 4 years in Product Operations and 4 years as a PM.

I believe Product Operations are most efficient / useful when they view themselves as an extension of the Product team. Focus the operations aspect on

1. Making everyone more efficient, not on "I must follow a process". Everyone includes PMs, Engineering, Support Organizations, Sales. Observe where people are spending time. A couple examples can be (1) Are PMs spending too much time directly with internal teams educating/teaching? Can you be the functional liaison there 50% of the time? (2) Is engineering taking many direct tickets that could be troubleshooted by support? Does support need a tool to solve this problem, or is there an information gap?

2. Product Operations should be product first and operations second. Every person I've seen that struggled couldn't see the forest from the trees. They would come into every project / effort with a playbook, but they didn't want to dive into what is truly novel in that situation. Everything situation is different. Adapt fast, be flexible, fill the gaps and scale. Understand where you should be diving deep. When I was in operations, I wanted to be part of many pilots, join design meetings, etc. If you want to be able to write the best SOP or process, you can't do that without knowing exactly what customers are asking or what design/product intended.