https://docs.papermc.io/adventure/minimessage/format/

{
    "timestamp": 1769112185945,
    "server": {
        "name": "Tildes MC - Season 3",
        "identifier": "bdf16729-1800-3b9c-9da5-833e8f70bc35"
    },
    "type": "chatMessage",
    "minecraftVersion": "1.21.11",
    "modVersion": "1.5.0",
    "payload": {
        "history": true,
        "uuid": "f5fc227d-6fca-32c6-8a39-3ccd59130ba9",
        "component": {
            "text": "Changed the text to: ",
            "extra": [
                {
                    "player": {
                        "name": "B__k_"
                    }
                }
            ],
            "color": "green"
        },
        "translations": {},
        "isPing": false
    }
}

In game looks like this

https://docs.papermc.io/adventure/minimessage/format/#head
https://minecraft.wiki/w/Text_component_format#Player_Object_Type

Two approaches

Render text we know, display ? or special character for things we don't know.

Something like Changed the text to: ? where the question mark might be red and on hover shows a text explaining that this is something webchat can't render.

Fully render playerheads and sprites

Player heads we can already do, so that seems feasible.
Sprites is a different story. We could possibly ship sprites with webchat, but I am not sure how that works with licensing. There is also the issue of new sprites being added to new games. Ideally we'd send over any sprites with messages or expose an endpoint where webchat can request sprites.

This obviously needs more investigation.