Portable foldable chair

Yes, it would be weird and impractical.

If you want to take a break in a piazza mid or late afternoon- a wonderful idea by the way, just go to one of the restaurants and order something to drink, and enjoy relaxing. If it’s during a mealtime, they will expect you to order a meal.

It’s an excellent idea to carefully choose your B&B or hotel for location which can be a huge benefit for your legs & feet. In small-to-midsized cities, I select lodging that is very close to the main cathedral or piazza. Then it’s easy to take a break whenever I would like to recharge myself & my phone, rest my feet for 20 minutes, and head back out ready to go again. I rarely need to use a bathroom besides the one in my small hotel, too. : )

We just bought folding chairs at COSTCO but they are chair size. Sitting to just watch the town’s people in their daily lives would not be appropriate. Follow the suggestions above, sit in an outdoor cafe and order drinks.

I cannot image a chair that folds to that size. Regardless, there are many places (nominally called 'cafes') in or near a piazza. Have a drink, a nosh and watch the world go by. But having your own chair to plonk down somewhere to people watch would be weird and distasteful.

A chair like that might be helpful in some situations such as waiting in line for something if you have issues with standing for longer periods of time. Also, in a museum or on a tour where you have to stand and listen to a guide or docent for periods of time - of course in that situation you would have to ask permission first. Otherwise, just to take a break and people watch, there are places to do that; cafes (as mentioned), park benches, etc..

In a piazza it would be weird, and it wouldn't even be allowed in front of many monuments, churches, etc.
They could be useful to visit museums, but I don't know if they allow you to sit on those inside museums. When I was a small kid in Florence, and the school would take us on our monthly school trip to a museum, sometimes (at the Uffizi for sure) they would give us miniature foldable chairs so that we (I was in middle school then) could sit in front of frescoes while the docent explained what we were looking at. That might have been an exception made for school kids, I doubt they would allow adults to do it, otherwise you'd see a bunch of German or American tourists with beach chairs admiring the Venus of Botticelli while sipping on a mug of beer and having a barbeque.

I love going on guided tours when I am traveling, but I also have a foot condition that makes it painful to stand for more than an hour or so at a time. I purchased a collapsible stool and now I won't travel anywhere without it. Yes, you will feel weird sometimes, and you may get a lot of well-intentioned but unwanted questions and attention from people who have never seen anything similar, but for me it allows me to travel pain-free. I have yet to be told in any museum or other site that I cannot use it.

Do you have a link to the chair ad?

Thanks for all the responses. The chair is called CLIQ https://www.cliqproducts.com/products/cliq-chair.
We won’t be bringing any chairs.

It's a camp chair with a back. You could find very similar for a third of the price elsewhere if you are considering one for some other use.

I sometimes use a cane for support. We were lucky to get Scavi tickets for our upcoming trip. After confirming by email with the Scavi site that canes--including ones that unfold into a seat--are permitted on the tour, I bought this to use: https://www.monoprice.com/product?p_id=43765
Yes, it will be embarrassing to use, but I plan to do so when I need to.