[FEATURE] Non-interactive mode for claude doctor

claude doctor exists as a CLI subcommand but requires interactive input (an Enter press) to complete. This makes it unusable from scripts, hooks, or from within a running Claude Code session (nested sessions are blocked).

It'd be great if it could run fully non-interactively, e.g.:

claude doctor --no-input     # run checks, print results, exit 0/1
claude doctor --json         # structured output for scripting

My use case: I have hooks/scripts that modify settings.json and want to validate the config afterward without opening a separate interactive session.