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/features/json_patch.md

@@ -3,10 +3,17 @@
 ## Patches
 
 JSON Patch ([RFC 6902](https://tools.ietf.org/html/rfc6902)) defines a JSON document structure for expressing a sequence
-of operations to apply to a JSON document. With the `patch` function, a JSON Patch is applied to the current JSON value
-by executing all operations from the patch.
+of operations to apply to a JSON document. Operations address locations in the document using
+[JSON Pointer](json_pointer.md) paths. With the [`patch`](../api/basic_json/patch.md) function, a JSON Patch is applied
+to the current JSON value by executing all operations from the patch, yielding the patched document as a new value.
 
-??? example
+!!! tip "Applying a patch without copying"
+
+    [`patch`](../api/basic_json/patch.md) leaves the original value unchanged and returns the patched result as a copy.
+    If the document is large and the original value is no longer needed,
+    [`patch_inplace`](../api/basic_json/patch_inplace.md) applies the same operations in place instead.
+
+??? example "Example: apply a JSON Patch"
 
     The following code shows how a JSON patch is applied to a value.
 
@@ -22,7 +29,15 @@ by executing all operations from the patch.
 
 ## Diff
 
-The library can also calculate a JSON patch (i.e., a **diff**) given two JSON values.
+The library can also calculate a JSON patch (i.e., a **diff**) given two JSON values with the
+[`diff`](../api/basic_json/diff.md) function.
+
+```mermaid
+flowchart LR
+    S["source"] -->|"diff(source, target)"| P["patch"]
+    S -->|"source.patch(patch)"| T["target"]
+    P -.->|"applied to source, yields"| T
+```
 
 !!! success "Invariant"
 
@@ -32,7 +47,7 @@ The library can also calculate a JSON patch (i.e., a **diff**) given two JSON va
     source.patch(diff(source, target)) == target;
     ```
 
-??? example
+??? example "Example: create a JSON Patch from the difference of two values"
 
     The following code shows how a JSON patch is created as a diff for two JSON values.
 
@@ -45,3 +60,11 @@ The library can also calculate a JSON patch (i.e., a **diff**) given two JSON va
     ```json
     --8<-- "examples/diff.output"
     ```
+
+## See also
+
+- [JSON Pointer](json_pointer.md) - the addressing scheme used for patch paths
+- [JSON Merge Patch](merge_patch.md) - a simpler, less expressive alternative patch format
+- [`patch`](../api/basic_json/patch.md) - apply a JSON Patch, returning the result as a copy
+- [`patch_inplace`](../api/basic_json/patch_inplace.md) - apply a JSON Patch without copying
+- [`diff`](../api/basic_json/diff.md) - compute a JSON Patch from two values