When I record a replay on a 1.18.1 client on a server which is running on 1.8.9, the player heads have the default Steve skin in the replay.

Cannot reproduce:

Update: I can see the heads when I have Automatic Recording turned ON. However, when I start the recording manually, the heads don't have the skins.

Interesting... I hadn't tried it on hypixel before and when I did just now, I found out that the heads work correctly there. Any idea what could be causing the placed heads not to have skins on a different server? It is only the heads that are placed in the world that don't have skins in the replay recording. A head in an armor stand loads fine.

This is an issue on any Spigot server according to my testing. You can reproduce it by creating a Spigot server on 1.8.9.

Spigot 1.8.9 by itself doesn't support 1.18.1. What exactly is it using to convert the packets for 1.18.1 clients? The Spigot ViaVersion plugin? BungeeCord ViaVersion? Velocity ViaVersion? Something else entirely?
Ideally you'd just provide me with a publicly accessible server address or a raw recording (from .minecraft/replay_recordings/raw/, corresponding to one which has the issue), so I don't have to set all that up myself.

Sure, you can try it yourself on play.survival-games.cz. Spigot and BungeeCord ViaVersion are used for packet conversion. There are some player heads on the ground as well as on armor stands on the main lobby.