Add `public` declarations

[mcabbott]

First commit adds only those in api.md, but perhaps we should add more... like Dual?

help?> ForwardDiff.Dual
  │ Warning
  │
  │  The following bindings may be internal; they may change or be
  │  removed in future versions:
  │
  │    •  ForwardDiff.Dual

(eval is following this https://github.com/JuliaLang/julia/pull/55097/files )