Do the posts for a carport sun shade need to be embedded in the ground?
There are no reasonably-priced post bases that will support your structure in that way. The post bases you describe are not intended for that purpose. They merely maintain post location and keep them off the concrete.
You need to either set the posts in the ground (to a depth of about 1/3 the above ground post height) or build enough diagonal bracing into the structure to make it free-standing. In the latter case you'd still want to anchor it to the ground to prevent lifting and tipover due to wind.