I can't use psql variable in the DO command. Is it intentional behavior?
yes. psql variables living on client side, and are not accessible from server side . DO command is executed on server side.
But SELECT command also executed on a server side )) I thought that the command is sent to the server after variable's replacement.
The psql variables are injected into SQL string before execution (before SQL string is sent to server). But this injection is disabled inside strings - and body of DO command is passed as string.