docs: migrate examples from JSON3.jl to JSON.jl v1

[s-celles]

Closes #1249.

JSON3.jl is deprecated. Migrate the two bundled REST-server examples to JSON.jl v1 per the official migration guide:

• JSON3.read(body, T) -> JSON.parse(body, T)
• JSON3.write(x) -> JSON.json(x)
• StructTypes.StructType(::Type{T}) = StructTypes.Mutable() -> removed
  (JSON.jl v1 auto-detects struct fields)

Add an explicit positional inner constructor Animal(id, userId, type, name) to both examples so JSON.jl v1's StructUtils can construct the struct from its parsed fields. The existing zero-arg Animal() constructor is preserved because the in-script client section still uses x = Animal(); x.type = ....

Add a regression test (test/examples_no_json3.jl) that walks docs/examples/ and asserts no .jl file references the JSON3 or StructTypes modules. This test was written first, observed to fail on the unmigrated tree (the TDD red step required by the project constitution), and turned green by the migration.

Two pre-existing example bugs were fixed along the way because they blocked end-to-end validation of the migration on Julia >= 1.12:

• The leading """...""" description in both files used to be parsed as a docstring attached to the following using statement, which Julia 1.12 rejects with "cannot document the following expression". Convert both to #=...=# block comments.
• cors_server.jl's intentional bad-path probe (HTTP.get(".../badpath")) raised on the 404 because HTTP.jl raises on error statuses by default. Pass status_exception=false so the example exercises the cors404 handler as intended.

Both fixes are documented under ### Fixed in CHANGELOG.md alongside the main ### Changed migration entry.

No public API of HTTP.jl changes. Project.toml [deps] is unchanged; JSON.jl remains a test/extras dependency only.