Context:
今日は仕事が終わってから、友達と夜ご飯を食べに行きました。ステーキのお店なのですが、食べ放題のパンも美味しかったです。食べ過ぎました。
I guess "のです"+"が" mean "although" or just "and then" here, and "～のです/～んです" expresses some kind of emphasizing, and the sentence pattern is "名詞だな＋のだ（です）".
(1) "な" in "お店なのです" is "連体形" of "だ", is it right? (2) May I ask why the "な" is necessary for the sentence structure? What is the difference between "ステーキのお店ですが" and "ステーキのお店なのですが" ?
The following two sentences are both correct and sound equally natural in the given context.
ステーキのお店なのですが、食べ放題のパンも美味しかったです。
ステーキのお店ですが、食べ放題のパンも美味しかったです。
The biggest difference is that the first (with の) would sound weird if said to someone who already knows the place in question is a steak house. This is because the first part of that sentence is meant to provide new information circumstantial to the statement in the second and main part.
The first part of the second sentence, on the other hand, simply states the fact that the place is a steak house, which may be already known to the listener.
The conjunction が basically plays the same function in both, but its adversative sense is felt stronger in the second as it puts one fact in contrast with another. With a little exaggeration, the second sentence could be translated as:
ステーキのお店ですが、食べ放題のパンも美味しかったです。
Despite the fact that it is a steak house, their all-you-can-eat bread was also good.
が in the first sentence (with の) is a weaker “but”.
ステーキのお店なのですが、食べ放題のパンも美味しかったです。
It’s a steak house, but their all-you-can-eat bread was also good.
な is required to connect this explanatory の to a noun or a な-adjective.
