Declare the documented public API via Julia's public mechanism (#1215)

[quinnj]

Supersedes #1215 (which targeted the deleted 1.x src/HTTP.jl and listed download/status — neither is an HTTP.jl function in 2.x).

HTTP.jl 2.x exports almost nothing (WebSockets, escape, and a few re-exports), so nearly the entire documented API is reached as HTTP.name without being formally marked public. Julia 1.11's public keyword exists exactly to distinguish supported public API from internals — this declares it, so downstream code and tooling (and names(HTTP)) reflect the real public surface. The retry_attempts/isrecoverable work from #1295/#1310 highlighted this gap.

What it does

• The main module, HTTP.WebSockets, and HTTP.Handlers each declare their documented, non-exported names public. Already-exported names aren't repeated. get/get! are included (they're documented HTTP.get/HTTP.get! entry points, even though HTTP extends them from Base).
• Gated on VERSION >= v"1.11.0-DEV.469" via Core.eval(@__MODULE__, Expr(:public, …)), which parses on Julia 1.10 (the package's lower compat bound, where the public keyword doesn't exist) — only the evaluation is version-gated.
• No behavior change: public does not affect using HTTP; it's metadata.

Validation

• names(HTTP) now surfaces 107 names (was just the exports); internals like _retryable_request_error/_normalize_local_addr correctly stay private.
• New test/public_api_tests.jl parses docs/src/api/*.md and asserts every documented HTTP.* name is exported-or-public (and internals are private) — a doc-parity guard so future documented additions can't silently skip the declaration. It already caught one gap during development (HTTP.@client).

🤖 Generated with Claude Code

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 87.16%. Comparing base (f8e9db6) to head (b6f7fae).

Additional details and impacted files

@@           Coverage Diff           @@
##           master    #1312   +/-   ##
=======================================
  Coverage   87.15%   87.16%           
=======================================
  Files          29       29           
  Lines       11291    11291           
=======================================
+ Hits         9841     9842    +1     
+ Misses       1450     1449    -1     

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