I am a fan of unusual mounts, but I know currently only a few animan companions have the Mount trait. So we need a new feat.
Beast Rider (General Feat 7)
Prerequisites : Ride, Expert in Nature, Mature Animal Companion
If your animal companion is at least one size category larger than you, you can treat it as if it has the Mount trait.
That would be imo overkill.
With just 1 general feat you are going to give a companion "special" perk to all other companions, which have different advantages in terms of attacks ( compare the Horse companion with a wolf companion which also has the "mount" trait, to see the difference in terms of AC, attacks, moveset, skills ).
Note also that you can already ride any companion ( once it's medium or large, depends your character size ). What changes is this
If it is carrying a rider, the animal companion can use only its land Speed, and it can’t move and Support you on the same turn.
Finally, with that feat, character would be able to ride a flying mount by lvl 8 ( using incredible companion with the savage specialization ).
Flying mounts are supposed to be a thing just by lvl 20 (currently, the champion is the only one allowed to have one, apart from being with the orc or half orc heritage, taking the lvl 9 "dragon grip" ancestry feat. But that would be up to the DM allowing it or not ).