For phone notifications that include icons or thumbnail images, the notification sync on my desktop initially displays the icon correctly. If an app updates its notification, though, kdeconnect only updates the text of the notification in its sync, not the icon. The result is that the desktop notification contains the new notification text from my phone, but the old icon, whereas my phone displays a new icon.

For example, a Twitter client that has a notification on my phone can update that notification as new tweets come in. The most recent tweet and the user avatar are displayed on my phone's notification. As new tweets arrive, both are updated. The desktop notification pop-up also displays the new tweet, but the icon it shows is always the first one shown since establishing the pairing with my phone. (If the connection is lost and re-established, a new, most-recent icon does appear.)

Another example: AppNotifier shows a notification on my phone when apps are updated, along with the app icon of the most recently updated app. Kdeconnect's desktop notification shows the correct text, but the icon is always for the first app that was updated, no matter how many apps have been updated since.

SOFTWARE/OS VERSIONS
Kdeconnect (Arch linux) 22.08.1-1
kdeconnect (Android 12.1) 1.19.1

Note: this is not a duplicate of the suggested bug 358677, as the notification itself is updated, it's just the icon that isn't.