Artificer Eldritch Cannon Protector temp hit points and Wildshape

I’m trying to understand how wild shape interacts with the temp hit points provided by eldritch cannon’s protector feature.

Here is the scenario:

  1. Artificer puts out eldritch cannon and gives temp hit points to the party
  2. Druid wild shapes
  3. Druid takes damage
  4. Artifcer re-applies temp hit points in the next round

My question is more or less order of operations with hit points. Does the druid wild shape carry those hit points and we remove that damage first? In this scenario every time the artificer applies temp hit points it buffs the wild shape form and allows for the druid to stay in wild shape much longer.

Or do we exhaust the wild shape hit points first and apply the temp hit points to the druid’s form that will be waiting for them after the druid breaks wild shape.

Essentially I need to know if temp hit points provided by the artificer allows for the druid to stay in wild shape longer.