So, turns out there is a way to open the console window from the Teams Client, hooray.
Right click -> DevTools -> Open DevTools (Select WebContents) -> Webview
Only problem? As soon as you change tab / reload a page, you have to repeat these steps. I really, really do not want to do this hundreds of times per day.
There, my question is this, is there a way to prevent that window from closing and simply updating depending on the tab that is currently selected?
Many thanks, fellow humans.
** EDIT ** Just to show that my tunnels are setup and the React app with the tabs starts properly in VSCode. I've used the MSTeams Toolkit VSCode extension to scafold the project.
If I run the app in Teams, I see my tabs content as expected.