Unify HandleException and PreCheckException

As it turned out, having two distinct exceptions, `HandleException` and `PreCheckException`, does not really provide any value. On the contrary, it makes some code more complex because both Exceptions can occur. Therefore, we should unify them.

Locate the definitions and usages of HandleException and PreCheckException, then trace the code paths where either exception can occur. Consolidate the exception handling and run the relevant existing tests; done means callers no longer need to account for two distinct exceptions and the test suite passes.

Written by the indexing model from the issue text.