Restaurants at at the Effiel tower

Without having eaten at them, the Tower's website should answer practically all of your questions about the two restaurants aside from recommendations of one over another:

https://www.toureiffel.paris/en/restaurants-shops

For instance, see the FAQ section of Madam Brasserie for dress code and getting to upper levels (no, not without a specific ticket to do so).
https://www.restaurants-toureiffel.com/en/madame-brasserie/faq.html

Jules Verne:
https://www.restaurants-toureiffel.com/en/jules-verne-restaurant/faq.html

I'm not including the Buffets, Macaron or Champagne Bar; those can be accessed with tickets to the corresponding levels. No dress codes for those, and no reservations.

This past April we ate at Jules Verne restaurant on the second tier. My husband wore black slacks with a collared shirt and black sneakers. I wore pretty much the same but shoes. People had all kinds of dress, no one stood out. But, we ate at 12:45. All the later slots were booked. It might be different in the evening. It worked out better because we saved quite a lot of € eating earlier. On that day we skipped breakfast and in the evening just had coffee and a pastry.
We did not have to wait on line as they have a separate entrance with a special elevator. After we ate we were able to go outside for the views. We did not go up to the top, I actually forget why.
Anyway, the food was very delicious, the extra cheese course was decadent, the service white glove, the staff extremely nice. When we return to Paris we will eat there again.

Jules Verne: This is what you need if wanting to go to the top after dinner (from the link in my last post):

"If you want to go to the Top of the Tower, you need to buy tickets online on the Eiffel Tower website or at the bottom of the Tower on the day of the reservation. You need to pick them up before going to the Jules Verne private lift. You will be able to go to the top of the Eiffel tower until midnight during summer, and 11pm for the rest of the year."