Simon:

That said, if there is no pending exception from the callbacks, the status returned by KINSOL
is ignored in release mode.
One solution would be to define the AssertKINSOL macro as "AssertThrow(...)", rather than "Assert(...)".

Yes, thanks for showing me a situation where this can happen! I made this into a test, and changed the Assert into AssertThrow here:
  https://github.com/dealii/dealii/pull/18428
I think that's what you had in mind, right?

Do you want to take a look whether the PETSC SNES and the Trilinos NOX solvers behave in the same way and perhaps also need to be fixed?

Best & thanks for the collaboration!
  W.

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