This is a common question, and the answer is usually on a case-by-case basis. The growth teams I’ve lead were typically a full-stack team consisting of growth, marketing, product, and analytics. Note that you will likely need design resources as well. They’ll typically prioritize their own backlog – though in some organizations, the prioritization has to be approved by senior leadership. The growth teams have to keep the larger organization up-to-speed with what was going on, so no one was caught off guard. This is of particular importance since the growth team will likely be the first team blamed if anything breaks.
When dealing with multiple products, embedding is typically the best option, but a central resource should exist to coordinate all the efforts and to ensure testing doesn’t overlap.
From an execution perspective, sometimes, growth teams run their own sprints, and sometimes they work through the typical product release sprints. It really depends on the type of product you are working on. Mobile apps for instance, don’t lend themselves to off-schedule releases, while web-based products do.
While working remote is definitely possible, it’s not ideal as it slows down communication and reduces the chances of productive water-cooler conversations.