fix(web): preserve task context and capability routing

[Qiyuanqiii]

Workbench flows could retain the wrong context after the frontend roadmap changes: extension settings returned to Inspector instead of the requested input area, new-draft image checks disagreed with the model chosen for creation, and unavailable historical Run directories silently opened the current/source directory. Desktop bootstrap also omitted the backend's GitHub review capability.

This patch opens the same task's composer while retaining its draft and attachments, aligns default image eligibility with selectable model routing, fails closed with a retry when a Run's directory cannot be confirmed, and forwards the missing Desktop capability. Go ownership, protocols and execution permissions remain unchanged. It also fixes a pre-existing transcript test race by waiting for the observed React Query update without weakening its assertions.

Related to #257. The acceptance report records the four reproduced defects, remaining candidates and evidence boundaries; this PR does not close the broader roadmap.

Validation after merging latest main 4de4a916837142bc3100e78f492b7b5b67ce2c57, including #288 and #293 (current head 1e614dbd031a6911abd23c55bbd148f53ce4f2be):

• The conflict in docs/PROJECT_MEMORY.md was resolved by preserving all dated checkpoints from both branches. The automatic application-navigation merge retains this PR's composer destination and the new recovery routing.
• 11 focused frontend files / 186 tests passed, covering navigation, attachments/image routing, historical directories, Desktop capability bootstrap, transcript updates, recovery navigation and GitHub approval flows.
• TypeScript and production build passed; merge-diff and conflict-marker checks passed.
• Applicable CI passed for this head: TypeScript console, Go checks and the Go control-plane gate. Unaffected checks were skipped by the existing classifier.

Original implementation evidence at 452b6fdcfd35c5049abc8b9e82c9390913cf6a5e (the browser experiments below were not repeated for this merge):

• Applicable CI passed for 452b6fdcfd35c5049abc8b9e82c9390913cf6a5e: affected-check selection, Go checks, TypeScript console and the Go control-plane gate. Unaffected checks were skipped by the existing classifier.
• 174 frontend test files / 1,656 tests pass (npm test -- --maxWorkers=4). Four app-navigation, three image-routing, historical workspace and Desktop capability regressions failed before their respective fixes.
• Production build, strict TypeScript, generated API/transcript checks, and existing Go documentation/release-contract tests pass.
• Actual production browser + isolated Go API: project import, unsent draft persistence through restart/reconnect, Inspector → extension settings → composer, and local stdio MCP registration/discovery/review/enable → composer pass without mocked browser responses. No task was created or executed by navigation.
• Initial full-suite runs exposed an existing Provider timeout under concurrent build load and the transcript notification race; the final full suite passes with the race fixed and the original timeouts retained.

The browser MCP peer is a deterministic local fixture. Native WebView2/GitHub login, real-model image/tool execution and the full model-to-preview/Git delivery journey are outside this acceptance slice.