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

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:
Terminal probes sent with `nvim_ui_send()` can reach more than one stdout TTY
UI. Probes with a known TTY UI owner should not accept `TermResponse`s from
unrelated UI channels. 

Solution:
Thread the existing `chan` filter through owned terminal probes. This covers
startup/attach background detection, fallback truecolor detection, and
`vim.tty.query()` forwarding opts to `vim.tty.request()`.

Note: Not every terminal escape path is updated here. I only passed `chan` when
the caller already knows which TTY UI owns the probe. For example, this does
not include:
- (Followup) OSC 52 (system clipboard) detection. It needs to capture the
  `UIEnter` channel. Adding `{ chan = ... }` only to the nested query would be
  half a fix.
- OSC 52 _paste_ is left global because the provider callback does not have
  a UI channel (paste is invoked without a ui channel/tty ui object).

Problem: Attach-time terminal probes cannot distinguish responses from
different attached UIs.

Solution: Identify the UI by RPC channel id in `TermResponse` and make
`vim.tty.request()` filter responses by channel.

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.

Problem:
- Windows users can't use terminfo to configure their terminal
  capabilities. #37274
- Terminfo definitions sometimes get out of date or are simply
  inaccurate.
- Eventually, we may want to drop terminfo, relying primarily on
  built-in definitions. Users will still need some flexibility.

Solution:
Support $NVIM_TERMDEFS environment variable, which is JSON data that
defines "terminfo" definitions that override our builtin terminfo.

Problem:
- Various `TermRequest` handlers which all do similar things.
- `tty.query` is specific to `XTGETTCAP DCS`, can't be reused for other kinds of terminal queries.

Solution:
Provide `tty.request()`.

Problem:
The `termcap.lua` module is too narrowly named. We may need a place for
tty-related functionality in the future.
https://github.com/neovim/neovim/pull/31399#discussion_r1882598297

Solution:
This isn't a public/documented interface, so just rename it.