Fetch and render files in the repository file tree browser

What does this MR do and why?

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

In this MR we fetch and render files for the repository file tree browser (blob and tree page). This enables basic navigation and functionality of the file tree browser.

Screenshots or screen recordings

How to set up and validate locally

⚠️ Please test it only from a tree view (navigating from overview/blob will not work as expected yet, we have issues for that).

1. Enable the repository_file_tree_browser flag
2. Navigate to either the repository blob viewer or tree list (not project overview)
3. The file tree browser should render

MR acceptance checklist

Evaluate this MR against the MR acceptance checklist. It helps you analyze changes to reduce risks in quality, performance, reliability, security, and maintainability.

Related to #541096 (closed)