Android's own feedback is the ripple, an ink circle growing from the touch point. TouchableNativeFeedback (Android only, one View child) takes background={TouchableNativeFeedback.Ripple(color, borderless)} or the theme's SelectableBackground(). Pressable has it built in as android_ripple, which adds foreground (draw over the children) and, for icon buttons, borderless with a radius:
<Pressable android_ripple={{ color: '#90caf9', foreground: true }} style={box}>
<Text>Pressable with android_ripple</Text>
</Pressable>
<TouchableNativeFeedback background={TouchableNativeFeedback.Ripple('#ffb74d', false)}>
<View style={box}><Text>TouchableNativeFeedback</Text></View>
</TouchableNativeFeedback>
<Pressable
android_ripple={{ color: '#a5d6a7', borderless: true, radius: 36 }}
style={{ alignSelf: 'center', padding: 12 }}
>box sets overflow: 'hidden' so the bounded ripples respect the rounded corners. The left screen of the figure in Wiring Up Buttons in BookNest shows the first ripple held under a synthetic long touch, drawn over the text because of foreground. iOS ignores these props, so add a pressed style there.