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