The “deflated balloon” gluten was most likely you mian jin, (油面筋) while the baked bran in the first dish was obviously kao fu. Yes, there appears to be dried bamboo in the first dish (too hard to see in the third one).
I’ve never seen the particular noodle dish you mentioned, but it doesn’t surprise me. Serving noodle soup with the intended toppings on the side (or “over the bridge”*) is definitely a common Shanghai, or more precisely Suzhou, thing, and how you combine the two is a user option. I’d be curious if the broth served with this particular dish was vegetarian.
I’d guess that the principals, or at least the chef, at Noodles Shanghai are from Jiangsu rather than Shanghai proper. Maybe the new wave of “Shanghai” cuisine is actually a wave of Jiangnan cuisine.
*The term “over the bridge” is not exclusively a Yunnan term, but in Suzhou there are no fancy stories to explain it; it simply refers to the motion of lifting the toppings from one bowl to the other with chopsticks. You can specify you want the toppings on the side with such a motion of the hand.
