Teams only show up on Stack Overflow. We will only see the new activity indicators if we first visit Stack Overflow, or make a habit of visiting the team itself. However, some users of teams do not use Stack Overflow: for example, most diamond moderators are a member of the Moderators Q&A team but most diamond moderators across the network do not visit Stack Overflow very often or at all.
Meanwhile we've got a sidebar with a lot of space on most other sites, and a site switcher to which we cannot add our teams.
Could users in a team have the capacity to add their teams to their site switcher or to their sidebar on non-SO sites?