I reviewed recently equella plugin and would like to add some comments.
First, there are some changes in repositories API and some other things that I noticed

Mostly they are not very big so I create one issue, feel free to split it or convert to META.

1. repository_equella::get_reference_details() is missing and we can not display the human-readable "Original" in Filemanager

2. please look at MDL-32474, there are new fields filepicker expects from repositories. In your case they are passed to M.core_filepicker.select_file()
There is also a function repository::prepare_listing() that converts dates to userdate, file size to readable size, etc.

3 (Moved to subtask MDL-33798)

4. Filemanager fails with an error often (I have to discover it a bit more)

5. When filepicker's select file window appears but you clicks 'cancel', an empty content is displayed.
Actually now when I looked closer I don't like the idea of calling parent.M.core_filepicker.select_file(). It is unsafe and may be prohibited in some browsers. I need to come back to this issue later myself, maybe will have to change API.