What is the problem this feature will solve?

This is a Meta issue to encourage contributors new and well-seasoned to consider where Astropy can use Exceptions with Notes.
One good category is wherever we catch an error, modify the message, and re-raise the same error, e.g. in #16878.

Describe the desired outcome

Please open PRs making our Exception messages more useful!

Additional context

EDIT: Would be much easier to wait for the following bumps first:

• requires-python = ">=3.11"
• pytest>=8.0

This change might also break downstream testing for our exception message with rigid match. Actual impact is unknown.