TL;DR, the Egyptian ghosts look like Davesprite (by way of Rick Riordan) as a gag.
Now for the full story...
Rick Riordan's Egyptian series first came out in 2010, when my obsession with Homestuck was just ramping up. Early on in The Red Pyramid, one of the main characters falls asleep and sees their spirit - or ba - leave their body. The ba was described as having a human head and a bird body. My HS-infested brain said, "That sounds like Davesprite!" and imagined all those scenes with Davesprites running around.
When I started conceptualizing HoT in late 2011, I thought it would be really funny if the ba in the comic looked like Davesprite. And though we're only getting to this scene in 2022... well, I just had to keep the gag. I still think it's really funny. And if you don't, well, enjoy these ghosts living the country club/resort life.