The search bar within Assets only works to search based on the fields visible on the Assets page, such as Name Values, Asset Type, Folder, User at the moment.
It should also work with other custom fields too (For example Serial number, Warranty End date etc....

How nice would be if Atera will fix the search Feature and will expand the search filter to all others fields too under Assets section.

I also contacted Atera support team and they confirmed about this issue and suggested me to vote here.