Replacing a document node on a webpage with React code using a browser extension

Question

I have a website that has a sidebar on it with way too many elements on it and I would like to write a browser add-on (available for as many modern browsers as possible) that lets users adjust the elements on the sidebar. Luckily I have access to the original React component that is used for the sidebar. I imagined the addon would work as follows:

1. A settings page allows users to design their own sidebar. For this, I believe I somehow must fetch the site content (which is probably React code) execute it (?), and find the node that I want to replace. Then I grab the elements on the sidebar to fill the default sidebar that the user can then configure to their own needs. Is executing the react code to get the elements the right approach here? If so, how would I do that?
2. When the user goes to the web page, a script is executed that will either find the dom element and replace it and update it each time the React Dom is updated (? not sure if that is even possible) or somehow locate the component in the React script and edit that. Again, not sure if that is even possible. An alternative would be to create an empty div and populate it with my custom component while setting the display property of the original component to none.

I would really appreciate it if somebody could let me know whether what I am trying to do is even possible, whether I am on the right track, and maybe can give me some hints on where to look for further information on how to achieve such a thing.