At the moment the file picker has many issues that make it not mobile friendly:

• button, icon, text, everything is quite small
• the popup should be static, fill the entire screen, ... there is no need to restrict the file picker to a portion of the screen neither it needs to be drag around the screen.
• the upload form is displayed by default but there is no need to display it. On mobile the user should click on the repository upload and it triggers the OS picker then the file form is displayed and filled up with the picked file info.
  ...

Obviously all this need specs first as it needs some brainstorming on the user behaviors/expectation and it also implies some technical challenges.