Share skills hook note post-processing (#2679)

* fix(integrations): share skills hook note post-processing

* fix(integrations): tighten skill post-processing

Apply skill content post-processing before the initial write, use an exact hook-note sentinel for idempotence, and route Copilot skill post-processing through the shared helper before adding mode frontmatter.

* Make hook note injection per instruction

* Deduplicate Codex hook note processing

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Co-authored-by: Puneet Dixit <236133619+puneetdixit200@users.noreply.github.com>
Co-authored-by: Puneet Dixit <puneetdixit200@users.noreply.github.com>