SHOW TABLE TYPES is a (to be deprecated) synonym for 
SHOW STORAGE ENGINES.
Fixed to use the right schema table in addition to 
issuing a warning.


mysql-test/r/show_check.result:
  Bug #30036: test case
mysql-test/t/show_check.test:
  Bug #30036: test case
sql/sql_yacc.yy:
  Bug #30036: use the right schema table