You are going to do 5-8% of the groups damage. I would not choose the healer for damage. I would choose the healer you enjoy the most keeping your group alive.
I can only speak for pve, as I haven’t touched pvp in a long time.
It’s MW monk, you can see for yourself at the top warcraft logs what they’re capable of.
As Tsjoh said you’ll be doing 5-8% of the groups damage if you all play equally well. If the group is bad you might get to 10-15% but the healer generally won’t be dealing much damage. In general the healers that do the most damage whilst also doing some healing is primarily MW, closely followed by disc priest, as they both heal through dealing damage. MW pulls ahead in raw damage though.
MW single target also gets buffed quite substantially going into the next season, so they’ll be doing a bit more compared to other healers. If damage is what you’re focused on, roll MW.
Here’s a summary of how current healer damage looks in m+, based on +10 Necrotic Wake keys:
Monks can do about 1000-1040k overall.
Evoker can do about 810-860k overall.
Disc priest can do about 680-710k overall.
Holy priest can do about 635-645k overall.
Paladins can do about 550-570k overall.
Resto shamans can do about 550-610k overall.
Resto druid can do about 550-580k overall.
A middle of the pack DPS can do about 2000-2200k overall.
These are all based of warcraftlogs, not the details addon. If you’re looking at the details addon you can probably add 20% dps to all examples.
In single target it’s a bit more fair, I think MW is about 32% stronger than the others.