So, if the steed is True Polymorphed into a statue, then its HP must be brought to 0 (by breaking the statue), or the Paladin dismiss the steed as an action before re-summoning.
When the steed drops to 0 hit points, it disappears, leaving behind no physical form. You can also dismiss your steed at any time as an action, causing it to disappear. In either case, casting this spell again summons the same steed, restored to its hit point maximum.
So, the spell True Polymorph turns that creature into stone. Concentration is held for an hour, the horse is a statue; but it is also still the spirit (creature) you summoned.
If you concentrate on this spell for the full duration, the transformation becomes permanent.
Both spells lasting effects are still in play, even though you're passed the duration. Nothing about true polymorph removes the effects of find steed. You should be able to still dismiss it, or drop its HP (objects have HP also) to 0 by breaking it. Devoid of either of those actions, the spirit is now a rock.
I'd like to think if the steed/familiar is dismissed to the pocket dimension remained a statue, because it is funny and I have no reason to believe otherwise. When summoned again, however, the spirit should assume the form of "an unusually intelligent, strong, loyal steed."
This way, none of the clauses of any of the spells were violated by the letter, and I believe intent, of the rules.
Also, permanent doesn't mean permanent. The effect can be dispelled by things like dispel magic, so I think ruling sending it back to the pocket dimension by dismissing it also releasing after the hour is a rational ruling:
True polymorph: recent printings of the PH clarify that "permanent" means the effect lasts until dispelled.