Kitchen exhaust fan
 

Any suggestions on exhausting cooking fumes from cooking area? Microwave vent just recirculates the smells and the fumes permeate into all rooms of our Gardenia. Thinking of ceiling exhaust since you cannot stack an exhaust hood over range/microwave complex(so I’m told).

OP, we have a Gardenia (2013) the microwave is definitely vented outside, the house plans also show a vent through the roof. I am guessing the microwave was not installed to use the vent. If you go in the attic you should be able to see the vent, same goes if you go outside you should see a rectangular vent. The microwave may have a plate that was not removed, this blocks the venting to the roof vent. Also, I have 'heard' some have a setting or switch for indoor to outdoor venting. The only way I know of checking for the plate is to remove the microwave and look at the back.
I would download the installation instructions for your microwave and see what it says about this.

or use Febreeze after cooking?

I'm assuming there already is a vent stack through the roof above the oven. If so, check the manual for your microwave. I've seen some that could be installed to either filter or exhaust fumes. You may need a different microwave if that's not an option with yours.

Developer cutting corners
 

My 1999 Villages model Stetson III, microwave does not vent outside, I can see no access on my roof, furthermore no venting to the roof for the bathroom exhaust fans.
I wonder if the Developer violated any building codes?

As mentioned above, some microwaves are vented through the back and connected to a duct that discharges the air to the outside. But, many of them vent through the vent holes at the top front of the microwave and discharge the air into the kitchen. The fan/duct assembly in the Whirlpool microwaves can be rotated within the microwave to discharge air either to the rear or to the top. So, you first need to verify if the builder installed exhaust ductwork from the microwave to the outside. If so, a simple adjustment to the microwave can solve your problem. If not, a ceiling exhaust fan ducted to the outside would probably be the best solution, but expensive.

Exhaust fans are most likely vented through the soffit at the nearest point.