You can interact with an object by merely using movement
The Basic Rules (and the Player's Handbook section you reference) specify:
You can also interact with one object or feature of the environment for free, during either your move or your action.
Since the Incapacitated condition only says:
An incapacitated creature can’t take actions or reactions.
You can still move, and therefore interact with an object or the environment when you do so.
Usually an incapacitated creature can't move anyway
Do note, however, that the most common cause of the Incapacitated condition is through other conditions like Unconscious:
An unconscious creature is incapacitated (see the condition), can’t move or speak, and is unaware of its surroundings
A paralyzed creature is incapacitated (see the condition) and can’t move or speak.
The creature is incapacitated (see the condition), can’t move or speak, and is unaware of its surroundings.
A stunned creature is incapacitated (see the condition), can’t move, and can speak only falteringly.
In these instances, as you can't move or take actions, you would be unable to interact with an object or with a feature of the environment.