WIP: Add ability to upload multiple files via UI

What does this MR do?

This MR improves current files uploading via UI feature.

1. It adds an ability to upload multiple files at a time.
2. It improves UX.

Are there points in the code the reviewer needs to double check?

To be added.

Why was this MR needed?

It improves UX.

Screenshots (if relevant)

To be added.

Does this MR meet the acceptance criteria?

• Changelog entry added, if necessary
• Documentation created/updated
• API support added
• Tests
  • Added for this feature/bug
  • All builds are passing
• Conform by the merge request performance guides
• Conform by the style guides
• Branch has no merge conflicts with master (if it does - rebase it please)
• Squashed related commits together

What are the relevant issue numbers?

Closes #13284 (moved)