Whata re the current support skills (and Icons)

[AdamFyi]

There is also Mantra from Pugilist it increases healing for groupmembers by 5%/20%

Oh thanks! I knew I was forgetting something. I'll add it to the list.

Convalescence isn't a support ability, it's a tanking C/D, albeit one of the weaker ones since it's used to recover from a big hit (or series of hits) rather than mitigate it.

Read. The. Post.
I mentioned it on the first few sentences that I listed down the actions that affect your party members directly, as per the OP's request. Convalescence increases the healing output received. Since this means that healers and any other source of healing from other party members is affected by this buff, it can be considered to affect the healing potential and therefore can be considered a support ability.