I don't recall that the cleaning of the car was at or close to the same time as the placing a bag of trash in the neighbor's bin. The FBI or whichever LE was watching the home did not need a warrant to collect the trash. I believe that once you put your garbage out for pickup, it's fair game for LE to collect. They could have collected several bags depending on how often their trash was collected for all we know.
It's possible the bag in the neighbor's bin contained meat and with BK's alleged aversion to meat, he didn't want it to even be in the family bin and that could also explain why he wore gloves when he carried it out. If it's true he didn't want his food prepared in cookware that had been used to prepare meat, he may have gone to further extremes with it. I doubt it but it's another way to look at it.
I believe the auto cleaning remnants, if any, were possibly burned in what looks to be a fireplace of some sort on the garage side of the Kohberger family home. He may have burned several things brought back from Pullman but that's just speculation on my part.
jmo