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

Extract the diagnostic implementation from
runtime/lua/vim/diagnostic.lua into focused internal modules covering
config, display, float rendering, jump/list helpers, namespace and
storage management, severity/shared utilities, and statusline support.

Move the builtin handlers into runtime/lua/vim/diagnostic/handlers/ and
keep runtime/lua/vim/diagnostic.lua as the public facade that lazily
dispatches to the split modules. This preserves the external
vim.diagnostic API while making the implementation easier to navigate
and reason about.

AI-assisted: Codex