Ensure file tree browser renders correctly without refresh when navigating between overview, blob, tree

Summary

This is part of a bigger effort to implement a file tree browser (FTB) in the repository.

As part of this issue we should ensure we can:

• Navigate from tree → blob via FTB without refresh done as part of !190487 (merged)
• Navigate from blob → tree via FTB without refresh
• Navigate from overview → tree/blob without refresh
  • the FTB should not render on overview page, but it should render on tree/blob when navigating from overview