fix(saver): propagate save failures to callers

[Sion612]

Summary

Saver.save() currently logs caught errors without rethrowing them,
allowing a failed save to resolve with undefined.

Rethrow the original error after logging so callers can handle the rejection.
Normal invalid-block filtering and the existing Tune error-handling behavior
remain unchanged.

Add regression coverage for synchronous Tool.save() throws, asynchronous
rejections, invalid-block filtering, and the existing rejection when saving
in read-only mode.

Fixes #3030.

Verification

Local validation of the reviewed candidate:

• Base implementation with the same regression tests:
  4 passing / 2 expected failures because save resolved with undefined.
• Fixed Saver spec: 6/6 passing in Chrome.
• Five related specs: 30/30 passing in Chrome.
• Separate production-build review: 5/5 Chrome checks covering retry,
  multi-block data preservation, validation rejection, existing Tune behavior,
  and awaited read-only transitions.
• Test and production builds, lint, and whitespace checks passed.
  Existing warnings were retained.

Full Cypress, Firefox, Edge, and a standalone TypeScript check were not run.
The separate review probes are validation evidence and are not included
in this PR.

This change does not implement automatic rollback of the read-only state
after a failed transition.

Implementation and local verification were AI-assisted.