The "+1 (555) …" pattern from every modern signup / login screen.
A 44px row with leading country selector (flag + dial code +
chevron-down), a 1px slate divider, and the digits input on the
right. Country selector is a button-shape (no actual dropdown
menu); caller handles picker UX as a separate concern. `value`
toggles between placeholder (slate-400) and populated (slate-900).