It isn't unfortunately. So first thing to understand: the React code doesn't live in VS when you open the solution. VS is not the best tool for editing React javascript. VS Code, for instance, is much better. So open up your Git cloned DNN folder in VS Code and go to the Admin Experience folder and then ClientSide. That holds all the React code for the PersonaBar. Navigate to the react project of your choice, for instance the Site Settings (SiteSettings.Web). Open the package.json and check the projects "name" (site_settings).
Now also open a shell/command prompt at the root of the git repo. And type in this code:
yarn watch --scope site_settings
This will fire up webpack and build this project and copy the result to where you've specified in the settings.local.json. If you don't know what that means please read the BUILD document in the repo documentation.
Peter