Properly update last action times in Idle Notifier

- Properly update last action times in Idle Notifier right after the
action is changed/updated.
- Do not reset lastCombatCountdown in resetTimers()

Supersedes/closes #6241
Extracted from #5369

Signed-off-by: Tomas Slusny <slusnucky@gmail.com>

runelite-client/src/test/java/net/runelite/client/plugins/idlenotifier/IdleNotifierPluginTest.java

@@ -155,7 +155,6 @@ public class IdleNotifierPluginTest
 		AnimationChanged animationChanged = new AnimationChanged();
 		animationChanged.setActor(player);
 		plugin.onAnimationChanged(animationChanged);
-		plugin.onInteractingChanged(new InteractingChanged(player, monster));
 		plugin.onGameTick(new GameTick());
 
 		// Logout