How to generate UID that will persist in both server and client side in nuxt?

Question

Maybe the heading is misleading, so I described my issue as thoroughly as I could.

I have a class that generates some id for itself.

class Div {
    id = null

    constructor() {
        // some more data
        this.id = id()
    }

    onMounted() {
        const HTMLElement = document.getElementById(this.id)
         
        HTMLElement.style.setProperty('--custom-property', 'lol')
        // do some stuff
    }
}

Then I render it on server-side (sorry for Pug):

<template lang="pug">
    .divs
        div(
            v-for="div in divs"
            :id="div.id"
        ) {{ div.data }}
</template>

After in onMounted hook I want to apply some dynamic generated stuff like styles or custom properties (as you can see above):

setup() {
    const divs = [
        new Div(),
        new Div(),
        new Div()
    ]

    onMounted(() => {
        divs.forEach(div => div.onMounted())
    })

    return {
        divs
    }
}

The problem is that the actual id's in array and in the DOM are different, so I got undefined while tring to call getElementById().

The reason why I am doing this is that I am creating a plugin and need these blocks to be rendered on server-side (by obvious reasons), but I need to set some custom properties because they will be provided by the end user. I don't think there is an other way to solve this, but I am open to any suggestions. Maybe it's a common issue that is solved already?

I also have no idea why id's are different, because I though that classes instantiated once on server, but it seems like they do it twice.