How do you create and chain custom exceptions?

Question presented to candidate: "Say you are writing a payments library. How would you design its exceptions, and when one of your functions catches a low-level error like a ValueError, how do you raise your own error without losing the original one?"

What a strong answer should cover:

• Subclass Exception (not BaseException), give the library one base class so callers can catch everything with one clause, and add specific subclasses for errors callers handle differently
• Extra data goes in attributes set in __init__, with every argument passed on to super().__init__ so args, str() and pickling keep working; override __str__ only for the message
• raise New(...) from original sets __cause__ (explicit chaining); raising inside an except block sets __context__ automatically (implicit chaining); the traceback wording differs
• raise New(...) from None sets __suppress_context__ so the internal error is hidden from the traceback but still kept on __context__
• add_note() (3.11+, PEP 678) attaches extra context to an exception after it was raised
• Chaining dates from PEP 3134 (Python 3.0) and from None from PEP 415 (3.3)

Clarifying questions expected:

• Who catches these errors: application code, an HTTP layer that maps them to status codes, or both?
• Do the errors need to cross process boundaries (multiprocessing, task queues), which requires pickling?

Code / implementation expected: Yes — a small hierarchy with one attribute-carrying subclass, and a function that translates a built-in error with raise ... from e.