This is a serious bug on the latest update 1.9.31.0.3. It is on legendary edition and is widely known as Brynjolf "hmm" bug or glitch. On some saves it is fixable by forcefully pushing him into the Ragged Flagen to start the rest of the mission. On others though the mission never starts. I have tried deleting add-on content and the saved data and re-installing them. I have also tried to do it only one at a time. I have done other missions that could be connected and have also tried pushing him into the Flagon. I have tried reloading previous saves and even leaving the quest for over 100 hours. This will not go away. And is extremely, extremely frustrating. The problem with this bug is when you get it it doesn't go away, and the information people have on it is limited. Getting Brynjolf to appear on the other side of the door is hard on its own, but when it doesn't even work after 3 tries. It starts to push your buttons. Please! Please fix this cursed hmm quest! At least make it where people can start it and push him into the Ragged Flagon! Please!

Maybe this helps:

I was having a heck of a time with this Brynjolf guy as well. I was suppose to meet him in the bar under the town but he just stood in the room outside doing nothing... I pushed him all the way across the room but he still just stood there. I entered the bar area and then went on into the next canol (or w/e) area and came back in. Voila! He was working again and he went to where he was supposed to.

Then after completing my next quest with him he was suppose to take me to the Thieves Guild leader, but no, I found him stuck in his stall still attracting everyone's attention like my first task with him was still going on. I figure that has been the problem, that script or w/e never stopped running.

He wouldn't move at all and I did various things trying to progress... eventually I shot an old woman in the head and he viciously struck her down for the insolence (of having the audacity to be shot in the head). My interpolation. Anyways, a guard comes to scold me and I bribe him, Brynjolf stops "attracting" the crowd, they disperse, and finally he leads me where I'm supposed to go. Seems all is well.

Moral: If all else fails, shoot an old lady in the head.