Overhaul how stashed diagnostics work, again.

Stashed errors used to be counted as errors, but could then be
cancelled, leading to `ErrorGuaranteed` soundness holes. #120828 changed
that, closing the soundness hole. But it introduced other difficulties
because you sometimes have to account for pending stashed errors when
making decisions about whether errors have occured/will occur and it's
easy to overlook these.

This commit aims for a middle ground.
- Stashed errors (not warnings) are counted immediately as emitted
  errors, avoiding the possibility of forgetting to consider them.
- The ability to cancel (or downgrade) stashed errors is eliminated, by
  disallowing the use of `steal_diagnostic` with errors, and introducing
  the more restrictive methods `try_steal_{modify,replace}_and_emit_err`
  that can be used instead.

Other things:
- `DiagnosticBuilder::stash` and `DiagCtxt::stash_diagnostic` now both
  return `Option<ErrorGuaranteed>`, which enables the removal of two
  `delayed_bug` calls and one `Ty::new_error_with_message` call. This is
  possible because we store error guarantees in
  `DiagCtxt::stashed_diagnostics`.
- Storing the guarantees also saves us having to maintain a counter.
- Calls to the `stashed_err_count` method are no longer necessary
  alongside calls to `has_errors`, which is a nice simplification, and
  eliminates two more `span_delayed_bug` calls and one FIXME comment.
- Tests are added for three of the four fixed PRs mentioned below.
- `issue-121108.rs`'s output improved slightly, omitting a non-useful
  error message.

Fixes #121451.
Fixes #121477.
Fixes #121504.
Fixes #121508.

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