Please read the advice shared on the Missing Animal Response Network. They have a page specific to lost cat behavior. The following search in a browser window will lead you to this site:
missing animal response lost-cat-behavior
I regret cannot provide the link directly, as I use to, as FB in all its wisdom is blocking the link as SPAM.
Next, If you have not already, visit neighboring homes (don't rely upon their reading a post), ask them to look into their garages and outbuildings, checking multiple times while sitting patiently, and quietly. Cats get scared when in strange places and won't necessarily bolt for the door when it is opened, and might not even run to a familiar person if they happen to be present.
Check every logical and illogical place your cat may have gotten into on your property, to name just a couple: cabinets/drawers — high and low; in garages/basements/sheds.
Don’t forget to check in with local vets and animal shelters.
Some have had success with placing a humane trap in their backyard - luring kitty in with a serving of their regular food; also with leaving clothing/blankets with your and/or their scent (if applicable).
Finally, for any reading this, please keep a bowl of water (ideally freshened every 2-3 days) in your garages/outbuildings for those instances when a neighborhood critter happens to find themselves trapped.
Good luck, I hope to read a positive update soon!