SUMMARY
I've used KDEConnect to transfer files from Android to Linux. I tried for the first time to go the other way, and no file ended up on Android because the app lacked permissions. It would be nice if the phone notified about the failed attempt.

STEPS TO REPRODUCE
1. Plug phone (mine is a Pixel 3) with KDE Connect app into laptop running KDE over USB
2. Pair devices if you haven't used KDE Connect before
3. In KDE Connect app, click ⋮ menu > Plugin settings, enable Share and Receive.
4. On laptop, click KDE Connect system tray icon, click ≡ next to phone name, click Share file, choose a video or audio file (over 1 MB so there's a progress notification).

OBSERVED RESULT
On Linux KDE desktop notification
   KDE Connect
   Sending to Pixel 3 (Finished)
appears, but there's no notification on the phone and when I check on the Android device using Files app there's no file.
It turns out I needed to grant the KDE Connect app access permission in order to receive files (details below).

EXPECTED RESULT
It's fine for sharing to fail, but ideally the phone would notify that receiving the file failed. When it works, the phone's notifications "window shade" includes
   KDE Connect·15m
   Received file from <laptopname>

Also the Linux side should not display a success notification; I filed separate bug 435241 for that.

SOFTWARE/OS VERSIONS

Linux/KDE Plasma: 
(available in About System)
KDE Plasma Version: 5.25.5 
KDE Frameworks Version:  5.79.0
Qt Version: 5.15.2 xcb

Fedora 33 package kde-connect-20.08.1-1.fc33.src.rpm
`kdeconnect-app --version` reports kdeconnect.app 1.0 

Android KDE Connect version:
KDE Connect version 1.16.0 installed from Google Play Store
Android Version 11 on Pixel 3


ADDITIONAL INFORMATION

I can't remember what I did the first time to grant permissions on Android. After revoking the app's permission in System Settings > Apps to reproduce, to grant permission the second time, I opened the app, click the name of the laptop, scroll down to
  "Some plugins have features disabled because of lack of permission...
  Share and receive"
tap "Share and receive", get a prompt to choose a destination directory, get a prompt "Allow KDE Connect to access photos and media on your device?, click its Allow, navigate to Download, and click [Use this folder].