Q.Dogwood tree trunk
Attached are some photos of my pink dogwood. The bark on the base last year came off, and now this is on the base. It is showing new growth already. I was wondering if this on the trunk was anything to be concerned with.

Yes it is of grave concern. It appears that the trunk was severely wounded and now wood rot fungal infection is present in the exposed heartwood. The bark peeling from the trunk at the higher point may be another wound, or could be a fungal infection due to the impaired circulation as a result of the lower wound.
Not much you can do but wait and see if it can overcome the wounding and infections. Provide good soil fertility and water management to enhance health and wound closure.
Pull back the mulch to 6 inches or more from the tree trunk, so it is not piled up against the trunk keeping it too wet.
If mine I would apply a biological fungicide as a soil drench around the base and also as a trunk drench. Now and once a month through the growing season. One of these:
https://www.domyown.com/companion-biological-fungicide-p-17627.html
https://www.domyown.com/cease-biological-fungicide-p-11636.html
https://www.domyown.com/monterey-complete-disease-control-readytouse-p-17485.html