Hey, I would really like to see my users' avatars in the web editor (/lp editor).
However, my server is non-premium and every player head on the list appear as Steve.

I suggest retrieving the Minotar skull not using an UUID, but the username instead.
This requires changing the URL from for example
https://minotar.net/helm/17257402-4aa4-36f4-adf4-c0fff91b8b7a/100.png
to https://minotar.net/helm/nickname/100.png.

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Retrieving avatars by username is deprecated, due to a) the Mojang ratelimits, and b) the fact that UUIDs are the recommended way to refer to specific accounts.

Offline mode players do not have real skins - that skin you posted is not in fact the skin of the offline player buty935, it is the skin of the real online mode premium player in question - therefore it would not make sense to display skins for them.

It is possible to fork & self host the editor if you wish to change this behaviour.

As mentioned by @codingJWilliams are username-lookups deprecated and most APIs to retrieve a players avatar/skin have removed such a support (with some exceptions).

The fact that your server is in cracked (offline) mode comes with such disadvantages, as the server itself wouldn't lookup the skin of a player either. You can simply check your tab list to see this effect in action.
On offline servers do tab lists not show the face of a player, while they do on online mode servers.

Your suggestion would imo not provide any useful improvements towards the web editor and would only make things more unreliable.

Thanks. I had no idea this would be such a problem.