What does the idler pulley do?

Hello,

The function of the idler pulley is to provide tension and guide the belt. Without the pulley it will not be possible to route the belt properly.
It has nothing to do with the engine's idle quality.

https://www.2carpros.com/articles/how-a-serpentine-belt-works

An engine can lose/burn oil due to having worn out valve stem seal, broken piston ring, plugged crankcase ventilation, overheating of the oil, also for having excessive block to piston clearance.

It will be best to look at each possible item and take appropriate action.

Please let me know if you have any questions.
Thank you.