I can't tell you much about how to download the file to Matcha. Here are a few workarounds I can think of to try out. What I would guess might be possible is that your documents never got uploaded to iCloud Drive from Matcha on your iPad. If Matcha was not uninstalled, the files should still be available on your iPad (not iPad Pro). If they are still on the iPad, you may want to try the synchronization again. It is also possible that you may be using a different iCloud account on the iPad than the iPad Pro.
I would suggest you first try to see what files you uploaded to iCloud Drive. Personally, I use Dropbox.
On your iPad, you can enable an iCloud Drive App to Navigate between your iCloud Drive files:
There should also be ways to access the files from iCloud Drive from Windows or Mac.
In the worst case, you should be able to access iCloud Drive files from your browser: