Can a creature be suffocated when using Hypnotic Gaze? [duplicate]

Can a creature that is charmed, incapacitated, and dazed using Hypnotic Gaze, be suffocated? Suffocation specifically states that the creature doesn’t take any damage until it runs out of breathe, and then its hit points drop to 0. If the method of suffocation doesn’t do any damage other than restrict the creature from breathing, would is still be considered that the creature doesn’t take any damage?

Hypnotic Gaze states (PHB 117):

Starting at 2nd level when you choose this school, your soft words and enchanting gaze can magically enthrall another creature. As an action, choose one creature that you can see within 5 feet of you. If the target can see or hear you, it must succeed on a Wisdom saving throw against your wizard spell save DC or be charmed by you until the end of your next turn. The charmed creature’s speed drops to 0, and the creature is incapacitated and visibly dazed.

On subsequent turns, you can use your action to maintain this effect, extending its duration until the end of your next turn. However, the effect ends if you move more than 5 feet away from the creature, if the creature can neither see nor hear you, or if the creature takes damage.

Once the effect ends, or if the creature succeeds on its initial saving throw against this effect, you can’t use this feature on that creature again until you finish a long rest.

With the rules for suffocation stating (PHB 183):

A creature can hold its breath for a number of minutes equal to 1 + its Constitution modifier (minimum of 30 seconds).

When a creature runs out of breath or is choking, it can survive for a number of rounds equal to its Constitution modifier (minimum of 1 round). At the start of its next turn, it drops to 0 hit points and is dying, and it can’t regain hit points or be stabilized until it can breathe again.

For example, a creature with a Constitution of 14 can hold its breath for 3 minutes. If it starts suffocating, it has 2 rounds to reach air before it drops to 0 hit points.

Charmed states (PHB 290):

A charmed creature can’t attack the charmer of target the charmer with harmful abilities or magical effects.

The charmer has advantage on any ability check to interact socially with the creature.

Incapacitated states (PHB 290):

An incapacitated create can’t take actions or reactions