Since updating to iOS 13 I have the same issue it seems. I can handoff from iPad to iPhone, but cannot handoff from my iPhone to iPad.
Handoff originally worked in both directions but after the iPad was shut down, handoff then stopped working from iPhone to iPad. The copy/paste clipboard between devices still works in both directions.
Tried turning handoff off and on again on both devices, restarting both devices, resetting network settings, turning Bluetooth and WiFi off and on again on both devices, signing out of iCloud and in again on both devices...all to no avail.
Start > General > Reset > Reset all settings on my iPad got it working in both directions again, but it doesn’t persist once the iPad has been switched off or rebooted (i.e. whether I shut down the iPad manually or when the iPad automatically reboots during the course of an iPadOS update - of which there have been plenty!). I’m then back to handoff only working from iPad to iPhone. The only way to get it working properly again is to reset all settings. But that’s a pain in the neck having to change all of the settings that have gone back to default.
Both devices are currently on 13.2.2 of their respective iOS and iPadOS.
(I have an open support case and Apple support took logs from both devices, but I’ve not heard from them since with any sort of update on the matter.)
iPad Pro 11”
iPhone 11