Fix LinkPicker freeze when virtual keyboard is hidden

packages/components/src/mobile/bottom-sheet/index.native.js

@@ -285,7 +285,10 @@ class BottomSheet extends Component {
 		const { height } = nativeEvent.layout;
 		// The layout animation should only be triggered if the header
 		// height has changed after being mounted.
-		if ( this.headerHeight !== 0 && height !== this.headerHeight ) {
+		if (
+			this.headerHeight !== 0 &&
+			Math.round( height ) !== Math.round( this.headerHeight )
+		) {
 			this.performRegularLayoutAnimation( {
 				useLastLayoutAnimation: true,
 			} );
@@ -551,6 +554,7 @@ class BottomSheet extends Component {
 					<View
 						style={ styles.header }
 						onLayout={ this.onHeaderLayout }
+						testID={ `${ rest.testID || 'bottom-sheet' }-header` }
 					>
 						{ showDragIndicator() && (
 							<View style={ styles.dragIndicator } />

packages/components/src/mobile/bottom-sheet/test/index.native.js

@@ -0,0 +1,24 @@
+/**
+ * External dependencies
+ */
+import { fireEvent, render } from 'test/helpers';
+import { LayoutAnimation } from 'react-native';
+
+/**
+ * Internal dependencies
+ */
+import BottomSheet from '../';
+
+it( 'does not animate transitions between header heights differing less than 1 pixel', () => {
+	const screen = render( <BottomSheet isVisible /> );
+
+	const bottomSheetHeader = screen.getByTestId( 'bottom-sheet-header' );
+	fireEvent( bottomSheetHeader, 'layout', {
+		nativeEvent: { layout: { height: 123 } },
+	} );
+	fireEvent( bottomSheetHeader, 'layout', {
+		nativeEvent: { layout: { height: 123.001 } },
+	} );
+
+	expect( LayoutAnimation.configureNext ).not.toHaveBeenCalled();
+} );