I've done some testing and with a haste 2 beacon and an efficiency 4 and 5 pick axe they don't instant mine stone. After some more testing I have discovered that even with 6, haste 2 beacons there is still no instant mine for stone.
Edit: I have discovered that the issue is that beacons do not give you haste 2. After using a command to give myself haste 2, instant mine worked just fine on stone. I was using a tier 5 beacon by the way. I have also discovered that when you give your self haste 1 it is called haste 2, and when you give yourself haste 2 it is called haste 3 in the effect menu. This has lead me to believe that even haste 1 from a beacon do not work.
Affects version 1.13.0 Bedrock playing on a Bedrock Realm on Galaxy S6 running Android 7.0 and also on Nintendo Switch. Even when the beacon is placed nearby the player, Haste II is not given correctly.