[codex] align distribution assets with sklt

[johnnyhuy]

This aligns the packaging and distribution assets added across the release/distribution work so the shipped package, installed command, and release artifact names consistently use sklt.

The npm flow had already been moved to sklt, but the companion distribution surfaces from the earlier packaging PRs still used skillet in binary filenames, package identifiers, formula/package filenames, container image naming, and documentation examples. That mismatch would have caused published assets and install instructions to drift from the actual CLI users now run.

This change updates the shared release target names, regenerators, checked-in packaging fixtures, and documentation for Homebrew, Chocolatey, winget, Docker, and npm-adjacent validation. It also fixes the Docker build context ignore rules so the renamed musl artifacts are still copied into image builds.

Validation:

• mise run test
• mise run build
• bun scripts/write-checksums.ts
• mise run render-homebrew-formula -- --version 0.0.0
• mise run render-chocolatey-package -- --version 0.0.0
• mise run render-winget-manifest -- --version 0.0.0
• mise run npm-publish-dry-run
• mise run docker-smoke
• mise run ci

Link-back PRs: #45, #46, #47, #48, #49.