Ambient chemical fumes can cause such an effect ... such as if the room the dryer is in, or nearby areas, are recently painted.

However, you describe the odor specifically as that of your laundry detergent, so seemingly paint isn't the cause.

Just because the vent is connected doesn't mean the exhaust ducting isn't clogged. Have you confirmed strong airflow is present at the outlet outside the house?

Your problem is due to either insufficient rinsing, too much detergent, hard water? First of all, if like so many other units, you have a FL that uses so little water there isn't a large puddle during washing and rinsing, you need to adjust the water pressure sensor (clockwise ) until the water level is increased to a reasonable level (barely up to the metal flange of the drum). Choose Extra Rinse for every load.

If you have a top loader, disregard the above.

the issue is not the dryer despite you thinking it is. :) something is amiss with the washing system.

I overlooked regards to my reply above that the dryer is electric. Gas dryers, not electric, are more likely to generate odd odors from pulling in ambient chemical fumes, due to the flame at the burner.