The brown patches on the foliage appear to be anthracnose, a very common fungal ailment of a variety of shade trees. They can cause a surprising amount of defoliation when infections are more severe; some maples and sycamores with this disease have been popular question submissions in recent weeks. Even so, trees typically recover well without intervention. Given the dry conditions found across the state, as you noted, we'd recommend making sure the tree has enough root moisture to reduce its stress and make it easier to produce new foliage, or at least retain the leaves it does have without some succumbing to desiccation. (Oaks might not shed infected leaves and leaf-out anew as readily as maple and sycamore would, and it's fine if it doesn't because most of the foliage tissue is intact to still photosynthesize more than enough to feed the tree for the rest of the season.)

The glossy-sticky residue is probably honeydew, and while it is fairly harmless by itself, it indicates the presence of a sap-feeding insect like aphids, scale, or spotted lanternfly. Aphids do not need management and plenty of beneficial insects consume them. Scale might, but only if abundant and causing plant dieback, as surprisingly high populations can be present for some time before any notable consequences manifest.

If in doubt, or before deciding on a course of action, have the tree assessed by a certified arborist who can help confirm a diagnosis and inspect the tree for pests of concern. They cannot treat every condition or cure existing disease but can look for indications of serious problems or determine when a minor pest just needs monitoring without immediate intervention. Some arborists are employed by tree-care companies (though not all tree-care employees necessarily have this level of training/certification) while others consult independently, in case you're worried about a bias towards recommending costly or unnecessary treatments.

Miri

Hello Judy,

You're welcome.
Neem oil is not effective for anthracnose or scale (most of the year, anyway) and is not practical to use to treat a plant of this size as the entire canopy would need good coverage from a spray. Neem also wouldn't be needed for aphids and would not be very effective on spotted lanternfly nymphs either, so while useful for other garden issues on annuals, perennials, or small shrubs, in this case it's not needed.

Miri

Thank you, and you're welcome!