This image was taken in January 2022, in the afternoon. The 46 via Bardi is the door immediately to the right of the Credit Agricole Bank.
https://maps.app.goo.gl/TKwRWrKkjukEesEb6
This is the same street, taken toward the opposite side. Still January afternoon.
https://maps.app.goo.gl/saye6CjixcEZ65gg9
As you can see traffic is minimum because the street is within the ZTL (Limited Traffic Zone). Only residents with permit (and mopeds) can enter, along with emergency vehicles and taxis. The only buses which go through there are the electric minibuses (basically vans), you can see one upcoming far in the background of the second image. At night there will be even less traffic. Obviously there might be the occasional noisy moped passing through, but I can't think of many streets where that will not happen. Unlike cars, mopeds can enter in most streets within the ZTL without resident's permit, that is why so many Florentines, of all ages, have one.
If you think that would be too noisy for you, you'll need to find accommodations in an alley. Try the hotel here. It's nearby but it's in an alley with zero traffic whatsoever. I've stayed here a few times, and it's very quiet. But even in the darkest alleys, you might encounter the occasional moped or vespa. That's a fact of life in Florence.
Lungarno alle Grazie and Lungarno della Zecca Vecchia (across the river from Piazzale Michelangelo) are NOT part of the ZTL, so obviously there will be traffic there. You can't compare that Lungarno with the ones inside the ZTL. The Lungarni east of the bridge Ponte Alle Grazie are outside the ZTL, as well as the Lungarni west of the Ponte Vespucci (except for the portion near the US Consulate which is closed to everybody for security reasons and where you will be shot if you try to drive in).