You are correct that the presence of actively feeding sap-sucking insects cause sooty mold. In this case, a type of soft scale is likely, though you can also look for aphids. We see what looks like frost-damaged new growth, so aphids on the new growth are less likely. You can look over the various types of common soft scales in the landscape here: https://extension.umd.edu/hgic/topics/soft-scales-trees-and-shrubs. A likely culprit is Cottony Camellia Scale (despite the name, they will also feed on holly); if so, there are control recommendations on this pest's page linked in the article. The sooty mold will gradually dry up and disappear as the source of its food, the insect honeydew, is eliminated.

Stressed plants can be more prone to insect outbreaks. The light conditions are fine for holly, though it's possible the roots were taxed by our recent aberrant weather patterns. Overly-wet and drought conditions alike can cause root death; root death can also result in plant malnourishment. We are not suggesting fertilizing; rather, monitor the soil in the plant's root zone when our weather becomes drier and periodically soak it well when we experience prolonged dry spells.

Miri