SOLVED: Skip to main content and Skip to footer links show in public site

Thanks for the link via DM. I can see the issue after some back-and-forth. As an intermediate fix,
add this to Bricks » Settings » Custom Code » Custom CSS:

.skip-link {
  all: unset;
}

.skip-link:not(:focus):not(:focus-within) {
    width: 1px !important;
    height: 1px !important;
    padding: 0 !important;
    margin: -1px !important;
    overflow: hidden !important;
    clip: rect(0, 0, 0, 0) !important;
    white-space: nowrap !important;
    border: 0 !important;
}

This unsets all default styles and adds new styles with a different approach (taken from Bootstrap 5.3).