Kitchen Sink Drain Help

I'm hoping someone can offer some expert advice. After I run my kitchen sink for about 10 seconds, the water level rises and drains very slowly (over hours). I have tried a vigorous plunger to no avail. I removed the water trap (clean, no debris), and confirmed no blockage between the sink and the trap. I used a 1/4" hand powered auger and can get to about 4' before I encounter resistance. At this point I am able to auger past but after withdrawing the snake I see no signs of anything really stuck in the screw and no improvement in draining. I have attached pictures of the plumbing. I have a few questions:

1. The third and fourth image show the same bend where my drain pipe attaches to the building pipe (runs vertically but cannot be seen in the picture). This is at about 4' and I presume this is where I'm encountering resistance with the auger. Is the picture just showing a fastener or is this some sort of trap? It's in a pretty inaccessible location and I'd basically have to take apart my kitchen counter to access it.

2. I'm wondering if the auger is encountering resistance at 4' because there's a bend or if there is a blockage?

3. If there is a blockage, I wonder if it is either in my pipes at that fitting or in the building pipes but my auger is going up instead of down. Is there a better way to go about approaching this problem?

4. Am I missing something entirely?

Welcome to the site.
Could be a blocked vent, check to see if people above or below that use the same pipe are having a problem.

WOW ... brass piping?? No ABS plastic with easily removable fittings?? Amazing setup.

1. Disconnect the fittings and dump the contents of the P-trap. Make sure it is clear.
2. Probe the pipe which goes toward the probable vent stack pipe. See if it has anything in it.
3. The plumbing into the vent stack looks incorrect but this could be the camera angle. There should be a fitting which conducts the water downward. It is is just a "T" fitting then the pipe will never drain as well.
4. If you can, run the thin auger thru the straight pipe and to the vent connection. This will certainly clear it.
5. It may be necessary to run a snake from the top of the building down the vent stack pipe to clear it from top to bottom.

kitchen sinks are usually blocked vwith grease and sludge.

you poke a hole thru it with the cable, but when yo pull it back, the hole closes again
call roto rootr or a drain cleaning co...have it scoured or jetted