I don't have the stats, but I think it fair to assume as you bind to more powerful steeds, the hps go up.
What I mean is Giant Bat or a Giant Eagle is likely to have more hps then a stag, war horse, pony, or war dog, and a Unicorn or Nightmare is likely to have more hps then a Giant Eagle or Giant Bat.
Also think on this, using the Fey Knight as an example, your steed will benifit, as long as your conscious, from Aura of Protection, that's your charisma mod to all your mounts saves, Aura of Warding (unique to the Oath of the Ancients), means your mount enjoys resistance against damage caused by spells. Cast Deathward on yourself and it will effect, your mount too, Death Ward means if you get hit by a save or die spell, you don't die or if you take damage that drops your hps to 0 you don't die. It lasts 8 hours, but it ends once it saves you. And of course Mounted Combatant is great. And if that fails you and your mount still ends up dead, cast find steed again and he's back with full hps.
A couple of cool spells that are interesting with your mount, the Avenger gets haste, which means if you cast it on yourself your mount is hasted as well. The Fey Knight gets Treestride which means you and your mount can walk into one tree and exit out another, once every turn for a minute. Fey Knight also gets stoneskin, resistance against Piercing, Bludgeoning, and slashing damage for an hour, as will your mount, Protection from Elements cast it on yourself and your mount benifits too, and Speak to Animals which will allow you and your mount to speak with animals, just some examples using Oath Spells.
