ALBANY, N.Y. — Mayor Eric Adams visited Albany on Tuesday to urge New York state lawmakers who hold sway over city resources to increase aid for the migrant crisis, asking for the state to cover 50% of the city’s migrant costs. The trip, an annual affair known as “Tin Cup Day” when city mayors make their demands of the powerful state Legislature, is Adams’ third as mayor and comes as thecity struggles to shelter an estimated 66,200 asylum seekers in some 216 shelters. “We are not out of the woods,” Adams, a former state senator, testified at a joint hearing of the state Senate and Assembly in …