When you play Jade Figurine, it does not trigger deathwish card effects.

I believe it should, you remove a card from the table, for any effect that unit 'dies' so it should trigger any kind of effect such action would.

In my opinion it's not a bug - the way it works is intentional, so you can bypass stacked effects on card. You don't kill this unit, you just transform it into other (jade) unit, then you remove it from a board. Transform does not equal kill. If you're familiar with Hearthstone, it works similiar to Polymorph card.

Polymorph keeps the card in play.

Jade figurine removes the card from play, hence destroys it.

I used Polymorph example of bypassing death effects. So if you're familiar with HS cards, Jade figurine works like Polymorph + Sap. Sap doesn't trigger death effects either.

Artefact Compression which creates Jade figurine states: 'Lock a unit and restore it to its base power'. And lock means 'disables a card's abilities', thus card works as intended.