Minecraft Bedrock Edition 1.14.6 - Test for specific potion type
Even though there's no NBT, there are data values for different types of potions.
You can use clear in a repeating command block to clear all the potions of a particular type and use a comparator to unlock the door.
Put this in a repeating command block:
clear @a potion <data value>
where the <data value> is one of the following (from the wiki):
┌─────────────────────────────┬─────────┬──────────┬──────────┐
│ Potion │ Regular │ Extended │ Enhanced │
├─────────────────────────────┼─────────┼──────────┼──────────┤
│ Water Bottle │ 0 │ │ │
│ Mundane Potion │ 1 │ 2 │ │
│ Thick Potion │ 3 │ │ │
│ Awkward Potion │ 4 │ │ │
│ Potion of Night Vision │ 5 │ 6 │ │
│ Potion of Invisibility │ 7 │ 8 │ │
│ Potion of Leaping │ 9 │ 10 │ 11 │
│ Potion of Fire Resistance │ 12 │ 13 │ │
│ Potion of Swiftness │ 14 │ 15 │ 16 │
│ Potion of Slowness │ 17 │ 18 │ │
│ Potion of Water Breathing │ 19 │ 20 │ │
│ Potion of Healing │ 21 │ │ 22 │
│ Potion of Harming │ 23 │ │ 24 │
│ Potion of Poison │ 25 │ 26 │ 27 │
│ Potion of Regeneration │ 28 │ 29 │ 30 │
│ Potion of Strength │ 31 │ 32 │ 33 │
│ Potion of Weakness │ 34 │ 35 │ │
│ Potion of Decay │ 36 │ │ │
│ Potion of the Turtle Master │ 37 │ 38 │ 39 │
│ Potion of Slow Falling │ 40 │ 41 │ │
└─────────────────────────────┴─────────┴──────────┴──────────┘
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Then put a redstone comparator next to it, which will output a signal strength equal to the number of items removed.