iOS Chrome supports “Add to Home Screen” since iOS 16.4.
You do still click a Share button, which looks like a box with an up arrow, but the button appears in the URL bar at the top of the screen in iOS Chrome; the URL bar might be collapsed, so the Share button might not be visible by default.
So, the message doesn’t need to change to say “Open it in Safari,” but it would be nice if it could correctly guess where the Share button is. On iPhone Safari, it appears in the center of the footer, which may be collapsed. On iPad Safari, it appears in the upper-right corner, not collapsed.
On iPhone Chrome, it appears in the upper-right corner, and might be collapsed. On iPad Chrome, it still appears in the upper-right corner, but won’t be collapsed.