Confirmed, and your observation about the bots is exactly what pinned it down.

The name plates for the local player and for NPCs are placed 4 pixels ABOVE the character's feet. The bots and other players are placed 2 pixels BELOW their feet. That 6-pixel difference is the whole bug — it's why your own tag and the NPC tags ride up over the legs while darkhunter92's sits neatly under his feet.

The cause was a misread of the original client. Its code does say "minus 4", but that number is handed to the text drawing routine, which then adds 6 more when it draws the dark plate behind the text. Net result in the real game: the plate's top edge is 2 pixels below the feet. Our name-plate component draws the plate straight from the position it's given, so "minus 4" put it 6 pixels too high. The remote-player code had independently arrived at the right answer, which is why the bots were the odd ones out.

Fix is one number: the offset becomes +2 instead of -4. That makes the player's plate land at exactly the same place the bots already use, and NPC plates drop to match.

Confirmed — your own name plate and every NPC's were riding 6px higher than they should, and higher than other players' plates, which is why they looked like they were cutting into the legs instead of sitting at the feet. In the real client the plate's top edge lands 2px BELOW the character's foot line (the name is drawn 4px above the feet, but the black plate behind it starts 6px lower again). Our remote-player plates already used that value; the local player and NPCs were using the raw -4 and missing the +6. Both now match.