Fix binary name and version references in documentation

[Copilot]

Documentation referenced incorrect binary name (coding-context-cli instead of coding-context) and outdated versions (v0.0.15, v0.1.0 instead of v0.0.16).

Changes

• Binary name: Updated all command examples from coding-context-cli to coding-context across README and docs
• Version: Updated installation instructions from v0.0.15/v0.1.0 to v0.0.16
• GitHub Actions: Fixed cache key to include architecture (coding-context-v0.0.16-linux-amd64) to prevent cache collisions
• Cleanup: Removed duplicate command examples in search-paths.md

Repository URLs correctly remain as coding-context-cli.

Before:

sudo curl -fsL -o /usr/local/bin/coding-context \
  https://github.com/kitproj/coding-context-cli/releases/download/v0.0.15/coding-context_v0.0.15_linux_amd64
sudo chmod +x /usr/local/bin/coding-context

coding-context-cli -s language=Go fix-bug

After:

sudo curl -fsL -o /usr/local/bin/coding-context \
  https://github.com/kitproj/coding-context-cli/releases/download/v0.0.16/coding-context_v0.0.16_linux_amd64
sudo chmod +x /usr/local/bin/coding-context

coding-context -s language=Go fix-bug

Original prompt

Review and update the docs.

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