The only time bard has ever felt like a support class in this game was back in 2.0 and Heavensward. Which is when you had a mana pool, 3 songs to choose from depending on the situation, which would result in a 10% reduction of damage (depending on the song) and some decision making to factor in.
As someone who has never played any Final Fantasy game outside of 14, Stormblood bard did not feel like a support at all because everything you did to 'support' the raid was everything any other DPS did in terms of buffing for raid-wide damage.
1.Battle voice doesn't feel like support because it's akin to any raid-wide buff you would hit on any other dps class.
2.Your songs giving a 3% doesn't feel like support at all because you would give the same raid-wide buff regardless of which song and when you played it. The 3% buff was a bi-product of playing the job correctly which ultimately makes it fall back into the raid-wide buff department like battle voice.
3.Any cross-class skill doesn't count (Refresh and Tactician) if you are arguing for identity.
4.Warden's paeon is never used in 99% of cases. The only time it has ever been used consistently was back in Heavensward for Warrior's berserk macro spam. If anything it's just reskinned Esuna.
5.Foes is somewhat on the fence but when you break it down it ultimately falls back into something like Battle voice since your only resource (mana) would be used for it and there's really no level of decision making either when using it.
6. Trobadour is debatable since you had to be in the right song for the right buff to go off which makes it hard to account for since the song rotation is very strict. If anything you had to pray the fight was scripted in a way that you could use it effectively.
The only big thing separating bard from being similar to other DPS buffing the party would be that it has more buffs than any other class in exchange for its lower DPS output.
If the criteria for 'support' is the number of buffs you can output in conjunction with low personal dps, it feels very weak as a criteria for the role of support.
Heavensward and 2.0 Bard is the best SE has ever done in terms of the identity of support because you had choice and had to have some level of decision making to play the class effectively for what it was intended. Stormblood bard doesn't feel like support because you buff the group regardless of what you did and, as a result, you had lower dps which made you 'feel' like you were supporting the group.
Edit: Nature's Minne was a decent support skill but it felt quite underwhelming unless you were in organised groups. In duty finder people would just overheal regardless.