Why was Earth's day stuck at 19.5 hours for 1.5 billion years?

Answer: Sun's air tide and Moon's ocean tide cancelled out

Sun's air tide and Moon's ocean tide cancelled out ✓ — Correct! The Moon's tide on the ocean normally slows Earth's spin. But the Sun also raises an atmospheric tide — and between ~2 and ~0.6 billion years ago, that solar air tide pulled in the opposite direction with almost equal force. The two cancelled. The day froze at 19.5 hours for 1.5 billion years, then lunar braking won again.

The core slowed until it matched the mantle's spin — Not quite. The core and mantle do couple — electromagnetically and viscously — and this can nudge day length by milliseconds over decades. But nothing about this coupling can pin the length of a day at a fixed value for a billion years.

Supercontinents formed, damping Earth's rotation — Not quite. Supercontinents do redistribute mass, which changes Earth's rotation rate very slightly via conservation of angular momentum — on the order of fractions of a second, not a fixed billion-year freeze. The real culprit was a tidal tug-of-war between atmosphere and ocean.