rough idle after restarting

1995 R1100RS 126k miles
For the last year or so I have noticed that after riding and the bike is warmed up to 5 bars, if I shut it down to get gas or take a break for the first 20 seconds or so the bike has a rough idle or has a had time running like it is bulking or starving for gas. I can increase rpm to 2k or 3k for 15 second while sitting and clear the issuse. This will happen even with a full tank of gas. The charcoal canister was removed about 10 years ago. I cleaned the BBS last weekend (very dirty) and then sync the TB with a twin max.

Do I have
1 an air leak in the tank fule line? no gas leaks on the outside lines
2 clogged fuel filter? 2 years old or 35k miles ish
3 something I'm just going to live with?

Assuming it idles well when cold, the first place I would look is the O2 sensor which sets idle mixture when the bike is hot.

Or maybe an injector is leaking into the TB.

Sometimes I have to add a little throttle when warming up from cold. (more plus the cold throttle advance/ choke)

It will miss/hick-up/sputter and almost stall when cold, warm or hot. Then settle into a good idle for about 3 min then miss/hick-up/sputter repete.

Roger is on the money; also, considering the age of the bike, I'd just go ahead and R&R both fuel filters (pump intake + main) and all the lines inside the tank: they deteriorate over time (especially with our alcohol'd gas) - make sure you use the HIGH PRESURE SUBMERSIBLE type (either BMW or Boneyard parts, or American spec J30R10). Last time I did mine (a couple of months ago), the inside lines "looked" fine along the outer jackets, but one was quite distorted inside.
How old is the air filter...

When you pull the brass screws, also either squirt some cleaner down the passageway (take out the lower/bottom sparkplug so the crud has an easy way to drain), or use a gentle Q-Tip with gas, alcohol, or cleaner on it to clear the bottom of that passage.

Also check the intake manifolds for a vacuum leak; you too, Red.

When I cleaned the BBS I pulled the rubber caps off the TB where one would connect the twin max hose to drain. I used carb cleaner and Q-tips until clean. When putting them back in a dab of oil on the O-ring to help slide it in. They were set at 2.5 turns left side and 1.25 turns right side. I had never touched them until the cleaning.
I put them back in at 1.5 off bottum and dead on in the middle with the twin max.

Looks like it will be time to open up the tank and go through it with freash parts.

Two bikes ago (97 1100), I put a little silicone lube on those O-rings...
Big Mistake! They were now fairly free to turn and wouldn't stay in adjustment.
Grrr...