I've converted many zombies into drowns and hunted them out in oceans, but none have ever dropped a single trident even after killing hundreds of them. I went into creative for a bit and used drowned spawn egg and those spawned with tridents and dropped them, but not naturally occurring ones or converted ones have ever.
Environment
1.13 Survival World, Java version, perfectly fine computer
Only non-zombie-converted-drowned have a chance to spawn weilding a trident, this chance is about as low as a zombie spawning holding a sword or shovel; and only when they weild a trident, they have a small chance to drop it (same chances as getting other naturally spawned mob equipment).
You’ve just been unlucky.