From Manifest Echo: “This echo is a magical, translucent, gray image of you that lasts until it is destroyed, until you dismiss it as a bonus action, until you manifest another echo, or until you’re incapacitated.”

From Hold Person: “Choose a humanoid that you can see within range. The target must succeed on a Wisdom saving throw or be paralyzed for the duration.”

From Paralyzed condition: “A paralyzed creature is incapacitated”

The echo disappears.

Jokes on you, my Echo Knight has a ring of free action!

Though as others have said (and as I’ve learned) Incapacitating an Echo leads to the disappearence of the Echo

A basic way to think about it, irrespective of the incapacitated bit, because the Knight attacks through the Echo, if the Knight can’t attack for whatever reason, neither can the Echo, whether it disappears or not.

Echo knight manifestations specifically are dismissed whenever you’re incapacitated. It’s one of the very first things mentioned in the description for the very first subclass feature they get.

You make your attack from your space or the echo’s space rather than the echo specifically attacking on its own. This is because you specifically have to take an action to attack, and Hold Person prevents you from taking actions. So RAW, if you are in a position where you cannot attack (such as by having Hold Person cast on you), you also can’t attack through your echo.

The echo doesn’t do anything by itself. All it does is serve as a placeholder on the map for you to perform attacks through, swap places with, and later on, observe through its position.

It’s not a separate creature that acts/attacks on its own, or anything like that. It also would disappear as soon as you’re Incapacitated.

Since all the echo actions are based on the echo knights actions, all the echo can do while the echo knights is paralyzed is move (since that requires no action).