Congrats on the new Mustang! To answer you simply: Yes, tuning will very likely void your Ford warranty.
While the Magnuson-Moss Warranty Act mandates that aftermarket parts themselves can’t void a warranty, it’s still perfectly legal for dealers to void warranties if a part impairs your vehicle’s systems.
Because tuning directly affects your ECU, it also directly affects what your ECU controls: the entire powertrain system. Therefore, most dealers will void any powertrain warranty if you install a tune—as it’s very difficult to prove that any damage to the powertrain system was not caused by that tune.