fix: prevent induction/cases from swallowing diagnostics when using clause contains by

[Kha]

This PR fixes an issue where the induction and cases tactics would swallow diagnostics (such as unsolved goals errors) when the using clause contains a nested tactic.

Closes #12815

[mathlib-lean-pr-testing]

Mathlib CI status (docs):

• ❗ Batteries/Mathlib CI will not be attempted unless your PR branches off the nightly-with-mathlib branch. Try git rebase e2b500b204cacbb3149f42feda880c8bdfcab7db --onto 6714601ee4a123fef0f6ff3e44f01086ba78dfce. You can force Mathlib CI using the force-mathlib-ci label. (2026-03-17 18:34:35)
• ❗ Batteries/Mathlib CI will not be attempted unless your PR branches off the nightly-with-mathlib branch. Try git rebase e2b500b204cacbb3149f42feda880c8bdfcab7db --onto 61a3443a9569d548a235f785b9a33984bb7ff622. You can force Mathlib CI using the force-mathlib-ci label. (2026-03-18 10:46:39)

[leanprover-bot]

Reference manual CI status:

• ❗ Reference manual CI will not be attempted unless your PR branches off the nightly-with-manual branch. Try git rebase e2b500b204cacbb3149f42feda880c8bdfcab7db --onto cfa8c5a036d6990635c6ec50b02d0e806995cec3. You can force reference manual CI using the force-manual-ci label. (2026-03-17 18:34:37)