Hi! I was leading a team that sounds like a similar role as you describe! Not quite ops, not quite SRE, but solving company problems and helping teams ship.
My team took over a traditional ops team, we were very much driving towards having application/product teams fully own their services in production. We built tools to help teams do this on their own (to varying degrees of success as the company grows). Nowadays, our problems are more focused on Enterprisey things like compliance and infra ops. We are an escalation point after product teams, and also offer support during all-hands-on-deck production incidents.
However, there are teams that have infrastructure needs and concerns and they need help from us, so we kinda "consult" with the teams and provide help to get them moving along.
We're a place where coders share, stay up-to-date and grow their careers.
We strive for transparency and don't collect excess data.