speakers work, all warning chimes do not?

The chimes in that car don't come through those speakers. They come from a speaker on the instrument cluster. The body control module senses whatever action like the door ajar, key in, seat belt and sends a signal to the cluster telling it to sound the chime. The most common reason for no chime is if the speaker failed. To repair it you have to remove the cluster and either repair it or replace it. To remove it you remove the upper trim from the steering column, then the screws from the cluster trim panel and pull to release the trim panel. Next remove the screws that retain the cluster and remove it. Unplug the connector.
Then plug in the repaired or replacement cluster.

Thank you, I checked a couple cluster repair websites but no one addresses the chime speaker. I also cannot find a replacement speaker.

Being that vintage you might be able to find a used one to replace it with but being a 2006 can make that difficult.