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

refactor(lua): add integer coercion helpers

Add vim._tointeger() and vim._ensure_integer(), including optional base
support, and switch integer-only tonumber()/assert call sites in the Lua
runtime to use them.

This also cleans up related integer parsing in LSP, health, loader, URI,
tohtml, and Treesitter code.

supported by AI

This commit also adds some tests for the existing memoization
functionality.

Problem:

`vim.validate()` takes two forms when it only needs one.

Solution:

- Teach the fast form all the features of the spec form.
- Deprecate the spec form.
- General optimizations for both forms.
- Add a `message` argument which can be used alongside or in place
  of the `optional` argument.

Memoizes a function, using a custom function to hash the arguments.

Private for now until:

- There are other places in the codebase that could benefit from this
  (e.g. LSP), but might require other changes to accommodate.
- Invalidation of the cache needs to be controllable. Using weak tables
  is an acceptable invalidation policy, but it shouldn't be the only
  one.
- I don't think the story around `hash_fn` is completely thought out. We
  may be able to have a good default hash_fn by hashing each argument,
  so basically a better 'concat'.