Date Lookup based on multiple columns in separate sheet

Since this is a large data set, I think the best approach is to perform an initial FILTER to pull relevant records to help make the XLOOKUP more manageable.

=LET(
    filtered, FILTER(
        HSTACK(AppID, date),
        (Activity = "Conversion Support") * (ActivityDetail = "Arrange Engagement Call") +
            (ActivityDetail = "Arrange Interview"),
        "None"
    ),
    lookup, TAKE(filtered, , 1),
    return, TAKE(filtered, , -1),
    XLOOKUP(all_app_ID, lookup, return, "", , {1, -1})
)