SameSite Cookie Header and Websocket not working

Question

Before we set sameSite: None our game did not work on any of the 3rd party sites. As can be seen in this video: https://youtu.be/_AYCvCrZyDk

The website loads but web-socket can not create a connection so everything is shown as loading... but the connection isn't established.

Then we added a sameSite: 'None' as can be seen below and everything started working.

export function setJwtCookie(res, userId: number) {
    const payload: IJwtPayload = {userId: userId}
    const newToken = jwt.sign(payload)
    res.cookie('jwt', newToken, {httpOnly: true, secure: true, maxAge: COOKIE_TTL, sameSite: 'None'})
}

But now small number of our players are complaining that they have the above problem if they are playing both on our site or 3rd part sites.

They tried different browsers, different wifi connections with the same computer but couldn't get it to work. When we upload a version without sameSite: 'None' they are able to play fine. So what is going on here? How can we make everyone play?

Here are the versions for convenience & testing. Thanks

1. Version with sameSite: 'None' included -> colonist.io
2. Version with sameSite: 'None' not included -> hexs.io
3. Iframe of colonist.io version -> https://iogames.space/colonist-io