It doesn't look harmful. From salivas moisture most likely. I would rinse in warm water, then dry, and apply a little coconut oil to add a barrier from the moisture.
Looks like dribble rash to me; my little girl has a rash around her chin and we keep applying a healing balm and it seems to be helping a little
100% dribble rash hun. no need to worry x
It def looks like a teething rash, or a dribbling rash as you called it. Um maybe try to keep it dry as best you can. I was gonna say if it doesn't seem like it's bothering her I wouldn't worry too much but since you stayed its been persistent for 3-4 weeks i think I'd wait maybe one more week with trying to keep it dry and see if it's worse or doesn't look any better I'd take her in. They might have something topical to put on it to help it.