So the URL structure would be something like this (illustrated with the
wishful thinking that we could acquire api.scheme.org one day):

     ;; R5RS PDF document:
     https://api.scheme.org/v1/r5rs.pdf

     ;; R5RS metadata as JSON:
     https://api.scheme.org/v1/r5rs.json

     ;; R5RS metadata as S-expressions:
     https://api.scheme.org/v1/r5rs.scm

     ;; SRFI 166 document as HTML:
     https://api.scheme.org/v1/srfi/166.html

     ;; SRFI 166 metadata as JSON:
     https://api.scheme.org/v1/srfi/166.json

     ;; SRFI 166 metadata as S-expressions:
     https://api.scheme.org/v1/srfi/166.scm

     ;; Information about the symbol call/cc as JSON:
     https://api.scheme.org/v1/symbol/call%2Fcc.json

     ;; Information about the symbol call/cc as S-expressions:
     https://api.scheme.org/v1/symbol/call%2Fcc.scm

     ;; Custom search for a symbol:
     https://api.scheme.org/v1/symbol/search.scm
         ?type=procedure
         &name=with-input
         &namematch=substring

The details are all subject to debate but that should give a taste of it.

Also, there is not much that is Scheme-specific (or even Lisp-specific)
to such an API, so if some other language community already has an API
we could just mimic their URL structure. I'm not aware of any such API.

There's Language Server Protocol (LSP) which is an open specification
from Microsoft, but as far as I can tell it's meant to be a personal
server to back a REPL session, not a public server on the internet that
serves the same content to everybody in the world.