To change Header height on Squarespace, you can follow these.
#1. You can edit Site Header
#2. Click Edit Design
#3. Scroll down and adjust Height
#4. Note
When you adjust to 0vw, but you still want to reduce the height further. You can use this code to Custom CSS box.
div.header-announcement-bar-wrapper {
padding-top: 1px !important;
padding-bottom: 1px !important;
}