And we dig deeper, what does UpdateCategoryAdCounts do?
I also researched a bit and realised that "clustered index update" means "using the clustered index to perform an update". Because of your trigger code accessing it by ID, that makes sense. I recall seeing index rebuild operations showing in the Query Plan if a clustered index (itself) is updated, which is not shown here.
I don't know how you will take to disabling the trigger, but try this
DISABLE TRIGGER [dbo].[classifieds_Ads] ON [dbo].[AdUpdated]
When the update has finished,
ENABLE TRIGGER [dbo].[classifieds_Ads] ON [dbo].[AdUpdated]
The trigger code is not efficient, but that could be another question.