Windows 10 player here. I am also experiencing the same bug. After farming over 1000 zombies converted into drowned I had no rotten flesh, gold ingots, nautilus shells, or tridents.
I then went to a creative test world and farmed an additional 200 converted drowned with a looting 3 sword and found that I still had not received any rotten flesh, tridents, gold ingots, or shells.
After that I spawned in 200 drowned with a spawn egg, then farmed them with a looting 3 sword again and I received a normal amount of the regular drowned drops.
I rely heavily on my drown conversion farm and it would really be appreciated if this was fixed.
After multiple different tests on Minecraft windows 10 edition version 1.10 I can also confirm that converted drowned drop nothing, and that naturally spawned drowned seem to be fine.
After farming nearly 1000 converted drowned from my drowned farm on my Bedrock dedicated server, the only drop I receive was the armor they are wearing before they are converted. I confirmed this in a test creative world as well and I got the same results.