Lot's of solid work here. A few thoughts:
1. Symphony of Battle and Delegation are too close to each other given that the latter will often make the former irrelevant. Alternatively having the Delegation give some other boost under the equivalent circumstances as a) it is a level 20 ability so if it stacks to be a little OP it's not a huge issue, and b) whether it is ever useful is pretty play style and DM reading dependant.
2. Not to seriously criticize the style of what is clearly a provisional write-up, but I think Inspiration should be renamed, because it is already confusing having both DM granted Inspiration and Bardic Inspiration, and this feels underwhelming when there is a direct comparison to Bardic Inspiration. The "able to take advantage" in Symphony of battle is also problematic wording given that Advantage is a major term of art in the game.
3. I love having any use for mental stats other than magic and skill checks, so kudos to all the subclasses.
4. I get that it is a capital S support class, but it still has way more buff others and not yourself abilities than any other class. I'd make the Warlord themself a valid target/beneficiary for most the abilities. It supports solo and small group play and it also makes sense on many of the abilities that the Warlord would know how to apply their tactical brilliance to their own actions and draw on their strength of personality to overcome their own adversities. As is they are, when there are no allies it is useful to help, more or less a strictly inferior Fighter. Talk about rubbing salt in the wounds that day when none of the other players show up.