Fixed #35233 -- Moved template engine system checks to backend methods.

Thanks Adam Johnson for reviews.

docs/topics/checks.txt

@@ -130,18 +130,18 @@ The code below is equivalent to the code above::
 
 .. _field-checking:
 
-Field, model, manager, and database checks
-------------------------------------------
+Field, model, manager, template engine, and database checks
+-----------------------------------------------------------
 
 In some cases, you won't need to register your check function -- you can
 piggyback on an existing registration.
 
-Fields, models, model managers, and database backends all implement a
-``check()`` method that is already registered with the check framework. If you
-want to add extra checks, you can extend the implementation on the base class,
-perform any extra checks you need, and append any messages to those generated
-by the base class. It's recommended that you delegate each check to separate
-methods.
+Fields, models, model managers, template engines, and database backends all
+implement a ``check()`` method that is already registered with the check
+framework. If you want to add extra checks, you can extend the implementation
+on the base class, perform any extra checks you need, and append any messages
+to those generated by the base class. It's recommended that you delegate each
+check to separate methods.
 
 Consider an example where you are implementing a custom field named
 ``RangedIntegerField``. This field adds ``min`` and ``max`` arguments to the
@@ -195,6 +195,10 @@ the only difference is that the check is a classmethod, not an instance method::
             # ... your own checks ...
             return errors
 
+.. versionchanged:: 5.1
+
+    In older versions, template engines didn't implement a ``check()`` method.
+
 Writing tests
 -------------