test: rewrite and run the AQE conformance workflow #347

Why

Windows and installed-target AQE lock proof moved here from #240 (ledger G13).

In scope

Rewrite the dispatch-only workflow (.github/workflows/aqe-m1-conformance.yml, kept at the annotated tag archive/completion-m1-workflow; the branch fix/completion-m1 is deleted) for ak init and the tool cache; dispatch on Linux, macOS and Windows with approval.

Out of scope

The shutdown leg, which waits on agentic-qe#801 (#396).

Acceptance criteria

• Busy startup and store preservation pass on all three systems
• Results recorded as a dated archive receipt

Dependencies

Blocked by: #335, #339, #240

Blocks: #385

Plan

• Release: 4.0.0-beta.1
• Size: size:M · Workstream: ws:remediation
• Epic: feat: project-scope P3, Codex and OpenCode project settings (epic) #298
• Card: P3-04 in the card inventory
• Sources: Supersession ledger (docs(plans): v4 GA master plan, supersession ledger and v5 registers #290) section H (WFL), G13

Verification

• Workflow run links