I noticed some green gunk near the warm and cold water shut off valves and the sink faucet. Does the condition of my water warrant for health concerns?
The corrosion is on the outside of the pipe, not the inside.
It's normal green copper oxides.
It says nothing good or bad about your water.
It says nothing bad or good about your water.
If you are on a municipal supply, ask them where you can see their required test results. They might even be willing to use your tap for one of their upcoming required tests (then again, with covid raging, they might not.)
If you are on a private well, send a water sample out for testing. That normally involves getting a kit of sample bottles with instructions. follow the instructions carefully - that is normally mailed to the laboratory, and they will email or mail results to you.