I've been following the research since December/January on New England Journal of Medicine, Virological.org, Lancet etc. And I think there is not yet enough evidence to suggest that there is immunity conferred by contracting Covid-19.
Does anyone know of any studies claiming that "herd" immunity is even possible with Covid-19? The latest article I could find is: COVID-19 and Postinfection Immunity https://jamanetwork.com/journals/jama/fullarticle/2766097
If there is no immunity or limited immunity conferred from infection then Covid-19 will be with the USA and other countries that have given up on control measures for a long time.