Calling it a “thing” because I don’t know the official terminology for it. It’s the reticle that appears when you move around on console.
Is there any API that I’ve missed that allows changing its image or disabling it?
Do you mean the cursor?
I just searched cursor on the create.roblox.com site and came up with this.
GamepadService | Documentation - Roblox Creator Hub
Don’t know if it’ll help you at all.
It’s virtual cursor. Disable it in StarterGui.