I have looked at the playground react code to see if any of the following bugs/issues could be easily addressed:

Line numbers overlapping with any query when the playground is first loaded
This issue is caused by the way components are being rendered by React and the way React handles CSS. Potentially the most difficult of the issues to solve as it will be quite involved to find the fix.

Removing unnecessary options such as: sharing playground, setting the endpoint, altering settings, potentially tabs
This is something we should discuss with product, but if we want to go down this route we may need to fork the repo or contribute upstream to make these things configurable.

Fixing the viewport so that the overall module fits better in our already tabbed component
Again, potentially CSS changes here which may not be easy. In its current form we essentially have a difficult to see toolbar at the bottom with Query variables and HTTP headers options. This is due to the viewport being set to the full screen as it was probably intended to be a standalone component and not embedded in a tabbed view.

I will raise any necessary issues upstream to hopefully gain some more insight.