Some pets float behind you. They dont flap wings or move on the ground. They float. Like the ghastly skull, or the Arcane/Darknoon Eye.
There used to be floating geodes but theyve all moved to the ground. Id love to find something Shaman-esque like the geode was that floats.
First pet that comes to mind is Mote of Nasz’uro:
https://www.warcraftpets.com/wow-pets/elemental/miscellaneous/mote-of-nasz-uro/
WarcraftPets has a filter for all pets that hover, but it also includes flying pets that flap their wings. Still, might be worth glancing through the list to see if anything fits your desired pet.
https://www.warcraftpets.com/wow-pets/filter/?all=Hovers,Y#
https://www.warcraftpets.com/wow-pets/filter/?all=Hovers,Y,Flying,N#
(this is the filter that excludes Flying pets)