I’ve been lucky enough to go to a few Michelin starred restaurants and I’d just do the suit thing tbh. Always better over dressed than under dressed.
As for being nervous, get over yourself, I found the staff to be very helpful and nice at these places and if you go in clearly there for a treat, i.e. this is special for you they’ll look after you.
I went to Enoteca Pinchiorri in Florence – 3 Michelin stars which was just amazing. I explained to the Sommelier it was a treat and we had no idea how to match a wine to the meal, he smiled and said, wonderful let me give you a different wine to match every course -there was like 8 courses- and he was bang on with every course. He loved it, loved showing us each wine and how it would go with a dish. The only glass we didn’t like was Crystal champagne, too flowery… ha, he let us finish it then replaced it with a different champagne, perfect, no charge, haha. These guys are just humans, very good at what they do but still just humans. Imagine them in their underwear… always a problem if shes a pretty lady! 😉