Fine webbing running up the trunk of a live oak in the South, with tiny spider-like insects underneath, is classic bark lice (psocids) activity. They are beneficial, not destructive.
Strong jet of water from a hose. That's it.
Reference: Auburn University Bark Lice Info
Sapsucker Damage on Oak Trees: Identification and Management
Sapsucker Damage on Young Oak: Same Culprit, Different Tree
Woolly Oak Aphid Infestation: Identification and Control on Live Oaks
Live Oak Bark Damage: Borer Diagnosis and Vigor Restoration
Borer Damage in Young Live Oak After Tropical Storms
Green Flat Fungus on Oak Trunk: Likely Lichens—Harmless, but Photo Needed for Certainty
Young Live Oak with Black Trunk: Scale and Fire Ants
Live Oak Decline After Pond Construction: Water Table Impact?
Bark Lice on Florida Oaks: Harmless Webbing Insects
Silver Oak Termite Damage: Internal Decay Likely Terminal
Spider Web-Like Cocoon on Live Oak: Need Photo for ID
Live Oak Tussock Moth Caterpillars: Identification and Management
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