Problem:

- annotation-usage-error and code-style-check are disabled.
- vim.inspect relies on a dummy self-assignment for docgen, and its help
  omits parameter and option details.
- LuaLS fallback types obscure iterator inference.
- Docgen hardcodes public function names and appends separately sorted
  files, leaving shared helpers under the inspector heading.

Solution:

- Enable annotation-usage-error and code-style-check, and fix misplaced
  annotations.
- Document vim.inspect's callable module directly, removing the dummy
  assignment. Describe its parameters, option defaults and process
  callback.
- Remove LuaLS iterator fallbacks, correct iterator signatures and check
  values that the improved inference identifies as optional.
- Parse callable modules, require bindings and parent module references.
  Derive public names and inherited function docs from these links,
  including missing help for vim.async.semaphore() and vim.version().
- Export vim.lsp.tagfunc directly with lazy loading and document its
  implementation instead of maintaining a wrapper.
- Group files in section_order, replacing append_only and merge_files.
  Merge declarations before sorting each section, placing shared helpers
  in the main vim section and keeping vim.inspect in alphabetical order.
- Add basic parser coverage for callable modules and module links.

AI-assisted

Problem: Argument type mismatches are excluded from EmmyLua checks.

Solution: Correct runtime annotations and calls, document local checker
workarounds, and enable the diagnostic.

AI-assisted

Enable EmmyLua's assign-type-mismatch diagnostic after correcting the
runtime annotations and assignments it flags.

Correct option, tuple, and return types, and use separate locals when a
value changes representation. Add guards and narrow casts where needed
so the runtime passes the stricter check. Regenerate the affected docs.

AI-assisted

Enable EmmyLua's need-check-nil diagnostic and resolve nullable values
through more precise types, explicit invariants, and guards for missing
runtime state. Keep analyzer-specific workarounds local and update the
affected API documentation.

Exclude the bundled re.lua from analysis so its nil-check warnings do
not fail CI.

AI-assisted

Enable checks for unused code, deprecated calls, return types, and
annotations.

Fix the warnings and replace the deprecated highlight function. Keep
exceptions where old APIs are still needed or the checker gets it wrong.

AI-assisted

Problem: LuaLS struggles with the generics used in Nvim's runtime,
requiring broad diagnostic suppressions. Indexing is also slow.

Solution: Use EmmyLua for type checks in the build and CI. It offers
more sophisticated type checking, substantially better support for
generics, and much better flow analysis.

Correct the affected annotations. Use `@internal`, supported directly by
EmmyLua, instead of `@nodoc` for shared internal declarations, and
support it in the help parser.

AI-assisted

Problem:
`inspect_tree()` documents `title` as
`string|fun(bufnr:integer):string|nil`, but the implementation handles
only `nil` and function values. A string title leaves `title` unset and
fails the assertion below.

Solution:
Use the string as the title.

Problem:
Cannot assign Lua functions/closures to "func" ('completefunc',
'tagfun', …) or "expr" ('foldexpr', 'indentexpr', …) options.

Solution:
- Store "func"/"expr" options as `Callback` instead of string.
- Delete oceans of copy-pasted code.
- BREAKING: LuaRef returned via RPC/Vimscript is now represented as
  `"<Lua N: file:line>"` (like what `:map` shows) instead of `nil`.
- Note: `man.vim` still uses `v:lua` string, bc it's a vimscript ftplugin.

Helped-by: Lewis Russell <lewis6991@gmail.com>

Problem:
`nvim_create_autocmd` is too verbose and its `callback` requires extra
"nesting".

Solution:
Introduce `nvim_on`. Start using it internally. Then we can get a feel
for how it should look before making it public.