Review and extend the documentation, and check it in CI (#5638)

* Review and extend the documentation, and check it in CI

A review of all documentation pages found factual errors, dead links,
missing cross-references, and gaps in examples. This fixes them and adds
checks so the same problems are caught automatically.

Fixes:
- wrong signatures and version histories (operator!= C++20 member,
  binary() subtype type, get<PointerType>(), JSON_NO_THREAD_LOCAL, ...)
- stale descriptions (number parsing since #5283, UBJSON table, SAX
  example that no longer compiled, tsl::ordered_map advice)
- dead internal and external links; repology.org badges (the domain is
  suspended) replaced by badges that query the registries directly
- deprecation notes link the migration guide; the guide itself fixed

Additions:
- "See also" sections, cross-references, 25 runnable examples, 12
  Mermaid diagrams, new API pages for json_pointer::operator<=> and
  byte_container_with_subtype::operator==/!=
- landing page, guides for untrusted input and performance
- "unreleased" badge after versions newer than the latest release

Checks:
- strict documentation build (broken links/anchors fail it); CI and
  the publish workflow fetch the full history the build needs
- weekly external link check, Mermaid syntax check in CI
- check_structure.py: example titles, heading levels, alt texts,
  header links, docset index coverage; its unused-example check works
  again
- all examples produce the same output on every platform

Signed-off-by: Niels Lohmann <mail@nlohmann.me>

* Keep the customer links that could not be fixed

A dead link on the customers page is still the evidence of where the
use of the library was documented. Keep the original URLs of the entries
without a working replacement (Marne, Cisco Webex Desk Camera, Philips
Hue, CyberArk) and exclude exactly these URLs from the link check.

Signed-off-by: Niels Lohmann <mail@nlohmann.me>

* Correct the duplicate-key recipe's claim about SAX positions

The SAX interface's key() receives no position either; only parse_error()
does. Also note that the recipe does not report the path to the repeated
key (see discussion #5085).

Signed-off-by: Niels Lohmann <mail@nlohmann.me>

* Say the library is available as a single header and mention json_fwd.hpp

Signed-off-by: Niels Lohmann <mail@nlohmann.me>

* Correct documentation errors found while hunting for bugs

- patch/patch_inplace: list the JSON pointer errors parse_error.106-109
  and out_of_range.402/404, and quote the actual parse_error.105 message.
- unflatten: list parse_error.106/107/108 and out_of_range.404.
- to_bson: list out_of_range.415 (binary subtype above 255) and note
  that 412 and 415 are new in 3.13.0.
- to_string: state that string_t must be convertible to std::string, also
  in the StringType requirements table.
- JSON Lines: a `while (input >> j)` loop also throws after the last value
  for concatenated JSON values; show a loop that works for both.
- BON8: a string gets 0xFF only if nothing follows it in the message; a
  string at the end of an array or object is ended by 0xFE.
- custom_string_type.hpp: add operator+=(char), which the "Always
  required" list asks for (json_pointer::to_string, flatten, unflatten,
  and diff did not compile), and an ADL int_to_string for diff and items.

Signed-off-by: Niels Lohmann <mail@nlohmann.me>

* Cache the release headers with functools.lru_cache

Codacy (Pylint) flagged the mutable default argument that header() used
as its cache. functools.lru_cache keeps the same memoization without it.
The script's output is unchanged.

Signed-off-by: Niels Lohmann <mail@nlohmann.me>

---------

Signed-off-by: Niels Lohmann <mail@nlohmann.me>

docs/mkdocs/docs/api/basic_json/operator_ne.md

@@ -9,17 +9,9 @@ bool operator!=(const_reference lhs, const ScalarType rhs) noexcept;  // (2)
 
 template<typename ScalarType>
 bool operator!=(ScalarType lhs, const const_reference rhs) noexcept;  // (2)
-
-// since C++20
-class basic_json {
-    bool operator!=(const_reference rhs) const noexcept;              // (1)
-
-    template<typename ScalarType>
-    bool operator!=(ScalarType rhs) const noexcept;                   // (2)
-};
 ```
 
-1. Compares two JSON values for inequality. Returns `#!cpp !(lhs == rhs)` (until C++20) or `#!cpp !(*this == rhs)` (since C++20).
+1. Compares two JSON values for inequality. Returns `#!cpp !(lhs == rhs)`.
     - This means the comparison is simply the logical negation of `operator==`, including for special values like `NaN` and `discarded`.
 
 2. Compares a JSON value and a scalar or a scalar and a JSON value for inequality by converting the scalar to a JSON
@@ -52,6 +44,11 @@ Linear.
 
 ## Notes
 
+!!! note "C++20"
+
+    Since C++20, `basic_json` declares no `operator!=`. The compiler rewrites `#!cpp a != b` as `#!cpp !(a == b)`
+    using [`operator==`](operator_eq.md), so the result is the same as described above.
+
 !!! note "Comparing `NaN` and `discarded`"
 
     Since `operator!=` is defined as `!(a == b)`, the behavior for special values follows that of `operator==`:
@@ -61,7 +58,7 @@ Linear.
 
 ## Examples
 
-??? example
+??? example "Example: (1) compare JSON values"
 
     The example demonstrates comparing several JSON types.
         
@@ -75,7 +72,7 @@ Linear.
     --8<-- "examples/operator__notequal.output"
     ```
 
-??? example
+??? example "Example: (2) compare JSON values with `#!cpp nullptr`"
 
     The example demonstrates comparing several JSON types against the null pointer (JSON `#!json null`).
         
@@ -89,9 +86,15 @@ Linear.
     --8<-- "examples/operator__notequal__nullptr_t.output"
     ```
 
+## See also
+
+- [operator==](operator_eq.md) comparison: equal
+- [operator<=>](operator_spaceship.md) comparison: 3-way (C++20)
+
 ## Version history
 
-1. Added in version 1.0.0. Added C++20 member functions in version 3.11.0. Changed in version 3.13.0 to remove 
-   special-casing for `NaN` and `discarded` values; `operator!=` now consistently means `!(a == b)`.
-2. Added in version 1.0.0. Added C++20 member functions in version 3.11.0. Changed in version 3.13.0 to remove
-   special-casing for `NaN` and `discarded` values; `operator!=` now consistently means `!(a == b)`.
+1. Added in version 1.0.0. Added a C++20 member function in version 3.11.0. Changed in version 3.13.0 to remove
+   special-casing for `NaN` and `discarded` values; `operator!=` now consistently means `!(a == b)`. Removed the C++20
+   member function in version 3.13.0; since C++20, the compiler rewrites `a != b` using `operator==`.
+2. Added in version 1.0.0. Changed in version 3.13.0 to remove special-casing for `NaN` and `discarded` values;
+   `operator!=` now consistently means `!(a == b)`. Since C++20, the compiler rewrites `a != b` using `operator==`.