Who is the better support and still can dish out dmg. Chongyun, Noelle or barbara?

The three characters you mentioned have very specific support roles so their damage output isn't that reliable or comparable to each other. For example, Barbara's damage output is abysmal but she can be a solid healer early on. Chongyun is more of a cryo-applier and off-field cryo sub DPS but then again, it will heavily depend on his equipment and artifact.

Noelle has the highest potential to deal greater damage compared to the other two. With DEF-focused equipment, full constellation, and Geo resonance with another character, she can be very tanky with her shield, can sustain the team decently with her heal, and can dish out high damage especially when enabled by team buffs and enemy debuffs.

At the end of the day, you can still make support characters deal decent damage with the right weapons, talent levels, artifacts, and constellations.