It depends on what tools you are using, but I believe that you are on the right track with your thinking about using your ticketing / issue tracking tool and providing appropriate views and filters.
I'm most familiar with Jira, but the way I handle this is that I create a new Jira project for the continuous improvement work, with its own workflows and issue types. Since we're scaled, I carry over the team field to this new project as well. I make sure that the filters for team boards look at cases where the team is set so it displays on the team's backlog and board views. For cross-team items, I don't set the team field. Everything, regardless of if it is on a team backlog and board or not, shows up in a backlog and board in the continuous improvement project.
Overall, it seems to work well. It gives transparency over what improvement efforts the teams are working on, and if two teams have similar objectives, they can coordinate, where coordination may mean working together or running two simultaneous experiments and discussing results at the end or something in the middle. It also lets us prioritize improvement efforts with product discovery and delivery work.