Excessive sap "bleeding" is typical when birch are pruned from late winter through summer; the best time to prune birch is from early to mid-winter. Prolonged sap production does not necessarily indicate an infection, and in this case, the pruning sap ooze is probably overlapping in its timing with the increased production of
honeydew from a sap-sucking insect. A likely culprit is
Spotted Lanternfly, which have been in your area for some time now but only as adults (which mature around midsummer and live until frost) do they produce enough honeydew to be more noticeable. You can learn more in the linked pages, but honeydew is essentially a clear, sticky, sugar-water based secretion the insects produce as a waste product. If Spotted Lanternfly are not the cause, then aphids, leafhoppers, and certain scale insects can produce honeydew, but they would not necessarily need to be addressed since rarely would they harm the tree enough to warrant insecticide use.
If you have tree health concerns, have it evaluated by a
certified arborist. Arborists can't treat or cure every condition, but can help narrow-down a diagnosis and look for sources of tree stress that might be able to be alleviated.
Miri