Squeaky sound coming from the brakes

Which sound? Could you post a video of it so we can hear it? Please.

Video is now up. Could you tell me which sound you mean? Is it the squeaking? If so that could be the brake pad wear indicator. Does it change sound if you lightly step on the brakes?

That would be the brake wear indicator most likely, it is telling you that you should check the brakes for wear. If the mileage you list is correct I wouldn't think they have worn out but I have seen a pad stick and cause strange wear before. I have also seen brakes that rusted apart from setting. To check them isn't that hard but you do need to jack up the vehicle one corner at a time so that you can remove the wheels and look at the brake pads close up. So say you start with the left front. You would break the lug nuts free with the wheel on the ground, then jack it up safely until the tire leaves the ground. Remove the lug nuts and the wheel. If it sticks in place turn so your back faces the wheel and kick the tire a few times, it should come free. Now with the wheel off you should see something like the picture. That is the caliper and the brake pads inside it. The red area would be the wear surface of the pad and the black is the backing plate. On the vehicle the wear material will likely be dull gray and the backer covered with rust. For an inspection the pad material will still pass even if it is very thin. However I like to replace them before that so I normally replace them when the red area in the picture is under 4MM or so thick. I also will replace them if one pad has more wear than the other, that can happen if the pads stick and only one is actually working. Another area to look at besides the pads is the rotors. You want to see the surface of the rotor wearing in a nice smooth pattern like the second picture. You can do this inspection at all 4 wheels.

This isn't your vehicle but the steps and methods are the same for replacing the front brakes. The rears are almost the same but smaller.
https://www.2carpros.com/articles/how-to-replace-front-brake-pads-and-rotors-fwd

Cost wise it all depends on the shop and what parts they use. The front pads cost from $25.00 up to $200.00 depending on which brakes it actually has. The rotors are about the same price range. If yours has the common brakes, I would say good rotors and pads would be about $200.00 for 2 rotors and the front pads. About the same for the rear. Then add in labor and you would be around $350.00 or so per axle, but it's hard to say for sure as some places use their own parts and have lower labor rates while others want to use OEM parts which will cost more, but they should also be the correct ones for the vehicle.

If they will, have them show you the worn parts and what they find. I'd hope it isn't the brakes in 35,000 miles but I have seen them worn out in less, especially in city driving where you use the brakes more than the gas.
Good luck.
Happy Thanksgiving to you and yours.