[Chore] Enforce safe async handling in core tools

[zoomote]

​Created by Roomote. Follow up by mentioning @roomote, in the web UI, or in Discord.

What changed

• Expanded the type-aware @typescript-eslint/no-floating-promises ratchet to core/tools/**/*.ts and resolved all 20 existing findings in that scope.
• Added explicit rejection logging for non-blocking command and MCP execution status updates while awaiting todo-list notifications that must remain ordered.
• Marked intentionally unawaited test callbacks explicitly and added branch coverage for parse errors, shell fallbacks, cmd.exe fallbacks, command timeouts, rejected webview updates, and edited-todo ordering.

Why this change was made

Floating promises can create unhandled rejections, silent status-update failures, and ordering races in tool execution paths. Enforcing the rule in this directory prevents new instances while making the existing asynchronous intent explicit. The focused branch tests also cover every line identified by Codecov's initial patch report.

Impact

There is no intended user-facing workflow change. Core tool execution is more resilient to webview notification failures, async ordering is explicit, and future floating promises in this scope now fail lint.

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.

📢 Thoughts on this report? Let us know!

[zoomote]

Addressed all five lines from Codecov's initial patch report with focused tests for parse errors, shell and cmd.exe fallbacks, command timeouts, and edited-todo ordering. Local coverage confirms each reported line is now exercised; the full lint, type-check, and test suites pass.

Pushed in commit 870112959. Codecov will refresh from the updated branch.