The Oozing effect and weaving effect (and probably the Infested effect as well) does not impact the Warden when it digs down. However, if the Warden is killed through conventional means, the effects function as expected.
Steps to reproduce
/summon minecraft:warden ~ ~ ~ {}
Toss an oozing potion towards it
Observed: No slimes spawned when the Warden dug down.
Expected: Slimes should have spawned.
The warden digging down is it despawning, not dying.