Why does a small steering correction keep a slow bicycle upright better than gripping the handlebars rigidly?

Answer: They steer the tires back under the falling center of mass

They steer the tires back under the falling center of mass ✓ — Correct. A small steering nudge turns the front tire toward the fall, bringing the tire's support back under the leaning center of mass. That is like shifting the base of an inverted stick toward the side it is tipping, so the bike can straighten. The bars are not held rigid because steering is what moves the support.

They lock the frame's lean angle so the bicycle cannot fall further — No. A rigid grip does stop the bars from turning, so it can feel as if the lean is being held. But it also removes an easy way to move the support point. When the bike starts to tip, the tires need to be steered back under the falling center of mass.

They use the spinning wheels' gyroscopic effect to push the bicycle upright — Not quite. The gyroscopic effect from spinning wheels can help bicycle stability a little, yet it does not explain why a slow bike benefits from steering correction. The rescue comes from steering the tires back under the falling center of mass, not mainly from wheel-gyro help.