Hi,
You have multiple CSS rules in your theme custom stylesheet file, which override the placeholder and the font sizes:
body #eut-theme-wrapper input[type="search"].orig::placeholder {
font-size: 10px !important;
}
body #eut-theme-wrapper input[type="search"].orig::placeholder {
font-size: 12px !important;
}
#eut-theme-wrapper input[type="search"]::placeholder {
font-size: 20px !important;
}
input.orig {
font-size: 17px !important;
}
There are probably more, but I could only find these at the moment. Removing these rules the font size will be the same on all devices.