use json_query,
SELECT @@SERVERNAME AS [Servername],
json_query(( SELECT [Name], [Recovery_Model_Desc]
FROM sys.databases
WHERE name in ('master', 'model', 'msdb')
FOR JSON PATH, WITHOUT_ARRAY_WRAPPER
) ) AS d
FOR JSON PATH, ROOT('ServerInformation')
SELECT @@SERVERNAME AS [Servername],
json_query(( SELECT [Name], [Recovery_Model_Desc]
FROM sys.databases
WHERE name in ('master', 'model', 'msdb')
FOR JSON PATH, WITHOUT_ARRAY_WRAPPER
) ) AS d
FOR JSON PATH, ROOT('ServerInformation')