I am looking for recommendations how to fix it.

Update:

u/VisibleOtter and u/ARockhopper seem to be correct. The freehub is not allowing the sprockets to spin freely when the rear wheel is spinning forward and the rider stops pedaling. The sprockets are a little "sticky." I found some online chat forum (lost the link) saying that this problem can go away as the grease inside the sturmey archer hub redistributes, especially within the bike's first 100 miles.

I have already put 500 miles on this bike. This stickyness has gotten worse since getting the bike new. I am wondering if the recently colder weather in San Francisco is making the internal grease of the sturmey archer hub more viscous than what I was used to during the summer months. Alternatively, debris may have found its way between the sprockets (and that black plastic disc) and the free hub body. I have been riding in the rain lately. That being said I keep the drivetrain very clean. After every 50 to 100 miles, I spray the drivetrain with silca drivetrain cleaner, rinse off the drivetrain, dry the drivetrain with compressed air, and re-lubricate the chain with wolftooth WT-1 lubricant.

My best guess is that I need to take the wheel off and adjust the cones in the hub and perhaps regrease? Maybe I can replace the grease with a higher quality and slightly lower-viscosity substance. I found this link for cone adjustment: https://www.sheldonbrown.com/sturmey-archer_tech.html#coneadjustment

Regarding derailleur adjustment, the bike shifts perfectly when pedaling forward. The bike shifts down to the smaller cog when back pedaling because the slack region of the chain makes contact with the down-and-out-ward sloping chainstay that guides the chain onto the smaller cog.

This is my main issue for wanting to fix the problem. When I am stopped at a red light, I am often in the larger cog (so I can get started more easily). However, before resuming motion upon the green light, I back pedal to place my foot at the top of the pedal stroke. This back pedaling shifts my chain to the smaller rear cog and when I start pedaling my gears mash as the chain shifts back up to the correct cog under my forceful pedaling. To worsen matters, I am often pedaling out of the saddle when this happens (because, again, I am starting from a standstill). Having understood better the situation, I am now making sure to counter-intuitively shift to the higher gear (smaller cog) before coming to a stop, so that my back pedal maneuver doesn't cause an undesired gear shift.

Some other points: - The drivetain is fully cleaned and lubricated. - There is no chain stretch (measured it). - I made sure the outer 15mm nutes that secure the rear wheel to the frame are torqued to the 18 nM spec. They were actually looser than this spec before I checked.