The Bug:

Being extinguished by water or powder snow inside cauldrons doesn't play the "Fire extinguishes" sound.

Steps to Reproduce:

1. Build the setup as shown in the attachment below. setup.png
2. Switch into survival mode and stand inside of the fire for a couple of seconds.
3. Approach and stand inside of the water or powder snow cauldrons in order to be extinguished from burning, and as you do this, listen closely.
4. Take note as to whether or not being extinguished by water or powder snow inside cauldrons plays the "Fire extinguishes" sound.

Observed Behavior:

The "Fire extinguishes" sound isn't played.

Expected Behavior:

The "Fire extinguishes" sound would be played.

Code Analysis:

Code analysis by Avoma can be found below.

The following is based on a decompiled version of Minecraft 1.18.1 using MCP-Reborn.

public class LayeredCauldronBlock extends AbstractCauldronBlock {
   ...
   public void entityInside(BlockState $bs, Level $l, BlockPos $bp, Entity $e) {
      if (!$l.isClientSide && $e.isOnFire() && this.isEntityInsideContent($bs, $bp, $e)) {
         $e.clearFire();
         if ($e.mayInteract($l, $bp)) {
            this.handleEntityOnFireInside($bs, $l, $bp);
         }
      }

   }
   ...

If we look at the above class, we can see that when an entity is extinguished in a water or powder snow cauldron, no method responsible for playing the appropriate sound is called, resulting in no sound being played.