Add abstract `SubTypeDiagnosticRule` to handle boilerplate type checking code.

At some point it might be cool to have a `SubTypeDiagnosticRule` where the constructor just takes `ExpandableStringEnum` (or the appropriate parent type name), and then calls into the abstract method to process when it matches. Not saying we should do it now, but it would be nice to avoid this code block every time.

_Originally posted by @JonathanGiles in https://github.com/Azure/azure-sdk-tools/pull/5935#discussion_r1160511750_

No files, tests, or entry points are named. Start by locating the existing boilerplate type-checking code and the relevant ExpandableStringEnum or parent-type handling, then determine whether an abstract SubTypeDiagnosticRule is appropriate; done means an agreed design and implementation path, not merely the proposed abstraction.

Written by the indexing model from the issue text.