where ESA is a polygon layer. Use PostGIS to test in/out

st_intersects_within.sql

-- inside ESA
UPDATE htmp points SET esa = 'yes'
FROM 
    (SELECT DISTINCT(poi.*)
    FROM vm_esa pol
    JOIN htmp poi
        ON (ST_Within(poi.geom, pol.geom))) inside
WHERE points.legacy_fulcrum_id = inside.legacy_fulcrum_id;

-- outside ESA
UPDATE htmp points SET esa = 'no'
FROM 
    (SELECT DISTINCT(htmp.*)
    FROM htmp
    LEFT JOIN vm_esa
        ON ST_Intersects(htmp.geom, vm_esa.geom)
    WHERE vm_esa.id IS NULL) outside
WHERE points.legacy_fulcrum_id = outside.legacy_fulcrum_id;