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I’m really looking for validation as to how I think this would work.

The Beacon of Hope spell description states (emphasis mine):

This spell bestows hope and vitality. Choose any number of creatures within range. For the duration, each target has advantage on Wisdom saving throws and death saving throws, and regains the maximum number of hit points possible from any healing.

Based on the spell description, I’m thinking any potion of healing would give the maximum HP as follows:

  • Healing – 10 HP
  • Greater Healing – 20 HP
  • Superior Healing – 40 HP
  • Supreme healing – 60 HP

I guess I’m not sure if it being a potion vs. a spell is relevant.

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Beacon of Hope affects any and all healing, including potions of healing

The beacon of hope spell states:

For the duration, each target [...] regains the maximum number of hit points possible from any healing. 

The potion of healing states:

You regain hit points when you drink this potion...

Thus drinking a potion of healing would count as healing and thus it would be affected by the beacon of hope spell.

Your calculations are correct, a common potion of healing would heal 10, a greater potion of healing would heal 20, a superior potion of healing 40, and a supreme potion of healing 60.

If they had wanted the feature to work a different way they would have phrased it differently like they did with the Life Cleric's Supreme Healing feature:

Starting at 17th level, when you would normally roll one or more dice to restore hit points with a spell, you instead use the highest number possible for each die...

This feature restricts the maximized healing to spells, but beacon of hope has no such restriction and so it works even on non-spell healing like the potions of healing, and even non-magical healing like the Fighter's Second Wind feature or expending Hit Dice after a short rest:

On your turn, you can use a bonus action to regain hit points equal to 1d10 + your fighter level...

A character can spend one or more Hit Dice at the end of a short rest, up to the character's maximum number of Hit Dice, which is equal to the character's level. For each Hit Die spent in this way, the player rolls the die and adds the character's Constitution modifier to it. The character regains hit points equal to the total (minimum of 0)...

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    \$\begingroup\$ I can just see the characters working on the plan: "Ok, it has been 59 minutes and 15 seconds. Activate Beacon of Hope, wait 45 seconds, then everyone stop short resting and expend hit dice." \$\endgroup\$ – Yakk Aug 28 at 19:03

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