registry: templated factory registrations inheritance

[zhxie]

Title: registry: templated factory registrations inheritance

Description:
Currently, factory registrations for base class cannot be used by their derivations. For example, an input Input registered for BaseClass cannot be created from a factory of DerivedClass. We do not have any precedence for these interactions with the existing extension registries, so it will be better if we can come up with a good solution to support shared inputs.

Relevant Links:
#20116

[kyessenov]

Another instance where factories might need to be smarter: custom tree matchers are specialized by DataType even though the matchers do not directly inspect the data. That means we have to register the same matcher for each possible DataType.

[github-actions]

This issue has been automatically marked as stale because it has not had activity in the last 30 days. It will be closed in the next 7 days unless it is tagged "help wanted" or "no stalebot" or other activity occurs. Thank you for your contributions.

[github-actions]

This issue has been automatically closed because it has not had activity in the last 37 days. If this issue is still valid, please ping a maintainer and ask them to label it as "help wanted" or "no stalebot". Thank you for your contributions.