Do I need to feed a mount summoned by Find Steed?

Find Steed reads:

You summon a spirit that assumes the form of an unusually intelligent, strong, and loyal steed, creating a long-lasting bond with it. Appearing in an unoccupied space within range, the steed takes on a form that you choose, such as a Warhorse, a pony, a camel, an elk, or a Mastiff. (Your DM might allow Other Animals to be summoned as steeds.) The steed has the Statistics of the chosen form, though it is a celestial, fey, or fiend (your choice) instead of its normal type. […]

That mount is a spirit, not a common animal of that type. Since the spell doesn’t go into details, I assume I don’t have to feed it as I’d have to feed a warhorse, for instance. However, do spirits need to eat in D&D?

The reason being: although celestials/fey/fiends most likely eat unless otherwise specified (ex: angels), they can be killed by bringing them to 0 HP.
On the other hand, a mount from Find Steed “disappears leaving no physical form” and can be brought back fully restored — basically, if it drops to 0 HP its body simply fades and it won’t die.
That fits the spirit part in the spell’s description and strongly indicates that it’s not just fluff, as it doesn’t work exactly like the usual celestials / fey / fiends nor the base animal.

The summoned spirit might come in the form of a celestial horse, but that doesn’t imply it actually eats like one, just like it doesn’t die like an ordinary horse or celestial.

The question: is there any factual or explicit rule to conclusively support a “yes, it eats/no, it doesn’t” answer?