After Floppy Hydra dies, and you play Umbra. Umbra’s trigger of deathrattles shuffles another copy of the hydra into the deck not Umbra itself.
Floopy Hydra:
Deathrattle: Shuffle a copy of this into your deck with permanent double attack and health.
Endbringer Umbra:
Trigger the deathrattles of 5 friendly minions that died this game.
triggering a deathrattle is not gaining a copy of it
You trigger the deathrattle of a floppy hydra, not your own
The source of the deathrattle is not the minion triggering it but the one having it
That’s a different behavior than repeating a battlecry where the source of the battlecry is the minion repeating it, not th eminion having it