ocaml-claude: defer README MDX side effects via let run ()
The three usage examples opened with [let () = Eio_main.run ...] which
mdx happily executed at test time, spawning the Claude Code CLI and
hanging dune test for 90s. Wrapping each in [let run () = ...] keeps
the examples type-checked against the real API without invoking the
Eio mainloop, restoring sub-second runtime.
While here, switch [Printf.printf] / [print_string] to [Fmt.pr] to
match the monorepo convention.