Adds explicit init --write support with backup behavior.

Scope:

• add init --write mode;
• keep init requiring explicit --dry-run or --write;
• reject --dry-run and --write together;
• keep init --dry-run read-only;
• create AGENTS.md when missing;
• back up existing AGENTS.md before replacement;
• avoid overwriting existing backups by using indexed backup names;
• preserve check console, JSON and Markdown behavior;
• add CLI and unit tests for write behavior.

Validation:

• ./scripts/check.sh passed with 50 tests;
• check console output verified;
• check JSON output verified;
• check Markdown output verified;
• init --dry-run on a new repository does not write AGENTS.md;
• init --dry-run on existing AGENTS.md does not write or create backup;
• init --write creates AGENTS.md;
• init --write backs up existing AGENTS.md before replacement;
• init --write does not overwrite an existing backup;
• init without mode returns exit 2;
• init with --dry-run and --write returns exit 2;
• no raw secret-like literals in changed files.