Checkout charged shipping after the bar said free

WooCommerce picks a shipping method again when the rates on offer change, and it picks the first one the zone lists. In a zone that lists Flat rate above Free shipping, a shopper who crosses the threshold keeps Flat rate selected, and pays it unless they notice.

Under Setup → Checkout → When free shipping is unlocked, choose Choose Free shipping for the shopper: Free shipping is then selected when the cart crosses the threshold, and the paid rates stay listed for anyone who wants a faster one. A shopper who was already past the threshold with a paid rate selected when you made the change keeps it until their cart or address changes. Or choose Show only the free options to hide the paid rates once Free shipping is available, for every shopper from their next cart update. Moving Free shipping to the top of the zone's list, under WooCommerce → Settings → Shipping, also makes WooCommerce pick it.

Choose Free shipping for the shopper works while the bar is on and reads WooCommerce's threshold. With an amount typed under Setup, free shipping comes from another plugin, and the plugin leaves checkout to it.

On WooCommerce 9.9 and later, Show only the free options is WooCommerce's own Hide shipping rates when free shipping is available, and the two stay in step. Being WooCommerce's, it keeps hiding the paid rates while the bar is off or reads an amount you typed. To bring them back, choose another answer under Setup → Checkout, or untick it under WooCommerce → Settings → Shipping → Shipping settings. On an older WooCommerce the plugin hides them itself, and only while the bar is on.