Is my dog’s licking when I bring my face close to theirs a display of affection or a manifestation of anxiety?
It depending on your dog’s individual personality.
Hello, let this not worry you any more since when a dog licks your face, they are performing a normal social behavior that can have different meanings like showing affection, asking for attention, soliciting food, or gaining social information. Licking your face can also increase their positive emotions and release endorphins. Licking your face is a way of saying “I ruff you” 
Dogs frequently express affection through licking, a behavior rooted in their instinct and the comfort they felt when their mother licked them as puppies. Licking is a significant aspect of how they bond with others, triggering the release of dopamine and endorphins that promote feelings of relaxation, calmness, and happiness.
That’s a cute and lighthearted way to look at it! Dog licking can indeed have various meanings and is often a sign of affection and social bonding. It’s a common behavior in dogs, and many pet owners see it as a loving gesture. As long as your dog’s licking is not excessive or causing any issues, it’s generally considered a normal part of their behavior.