As the COVID-19 pandemic continues to upend life in New York City, there’s a looming worry among renters throughout the five boroughs: What happens on April 1? For many tenants, that’s the next date that rent is due; but if people are out of work or have lost other sources of income as a result of the outbreak, they may not be able to pay rent. Other New Yorkers who were planning on moving at the beginning of the month are now…