bugfix: Enforce and document context injection into custom callbacks

[ferruzzi]

Found a bug while manual testing deadline alerts. We are now injecting context into custom callbacks, but if the user didn't add context or **kwargs to their custom callback, it will fail with an unexpected parameter exception. We can either document that all custom callbacks need that, or we can add guardrails so context is only provided if it is supported. I figured the latter was more robust and safer. New code filters parameters going into any custom callback to only provide parameters it expects.

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[ferruzzi]

followup to #61153