The cottony material is likely cottony aphids (or cottony cushion scale). Touch it—if it moves, it's insects. Sticky honeydew on leaves confirms sap-feeding.
Systemic treatment is most practical for homeowners. Apply per label; honeydew and sooty mold will disappear once insects are controlled.
Globe Willow Honeydew and Sooty Mold: Aphid or Scale Control
Black Sooty Mold on Littleleaf Linden: Aphid Control Strategies
Littleleaf Linden Honeydew: Aphid/Scale Systemic Treatment
Maple Honeydew Deluge: Neighborhood-Wide Aphid/Scale Outbreak
Live Oak Roots Lifting Sidewalks: Engineering Solutions
Pink-Striped Oakworms on Live Oak: Minor Late-Season Pest
Sticky Sap Dripping from Oak: Aphids or Scale
Live Oak Too Close to House: Get Professional Assessment
Black Leaves on Ornamental Pear: Sooty Mold from Aphids
Cottony Substance on Oak Leaves: Cottony Aphids
Black Walnut Honeydew: Aphid Control on Large Trees
Crepe Myrtle Sooty Mold: Aphid Control Eliminates Black Fungus
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