The problem with the former is that what you’re doing is USE 'myDB'
rather than USE myDB
.
you’re passing a string; but USE is looking for an explicit reference.
The latter example works for me.
declare @sql varchar(20)
select @sql="USE myDb"
EXEC sp_sqlexec @Sql
-- also works
select @sql="USE [myDb]"
EXEC sp_sqlexec @Sql