Fiat 500 - Brake noise after encounter with puddle

Vehicle brakes have been designed to allow for operators driving through deep water. Your vehicle likely has disk brakes, which are made of a steel alloy that rusts if you look at it crossly.

It sounds from your description that your brake disks have collected a bit of overnight rust from being wet. The scraping sound is the brake calipers scuffing off the rust, which is also provided for in the design.

I have a vehicle that is rarely driven and the disks will collect surface rust which is shortly scuffed away in normal braking.

I use the term "collect" but the reality is that some of the surface is converted to rust by exposure to the air and to moisture. Rust never sleeps.

More extensive reading can be found on the 'net, but the results of my search provide the same conclusion. Here's one with a bit of commented discussion.

https://www.quora.com/Is-the-rust-on-the-surface-of-a-cars-brake-discs-a-bad-thing

I can attest to this possibility as it happened on my car and I did my own repairs so I know that caused same in my vehicle. If you don't know disc brakes work by a rotor attached to your wheel/tire and a set of two pads, one on each side of the rotor, that are clamped and squeezed when you press your foot brake pedal. Though hugely rare it is possible that a pebble, albiet a small one, can get jammed in between the pad and the rotor and unable to dislodge and thus makes perhaps continuous noise that gets much worse the harder you pump the brakes. In normal instances this pebble get worn away quickly and the noise goes away. For me the pebble that lodged itself into my brake rotor/disc was a lot harder than the metal of the steel rotor and by the time i got tired of the noise and removed the pads the very hard iron pebble has worn a nice 1/8 inch groove into my disc rotor and likewise damaged the brake pad, so even though my brakes were relatively new I had to buy a new rotor and pads for that front right wheel of the vehicle to fix the damage. I should mention that a similar but less expense cause might be a rock that has managed to get itself lodged between the disc rotor and the dust sheield of the wheel allowing the rock to grind against the wheel or rotor or both.