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

Problem:
A blank line before the Content-Length header makes header parsing
fail with "Content-Length not found in header". An LF in the 'name'
state falls through to the 'invalid' state, which only return to
'name' at the *next* LF. That LF terminates the next line, so the
line with Content-Length is swallowed.
The same issue happens when a junk line is a partial match of the
header name (e.g. "Cont\nContent-Length: ...").

Solution:
When seeing an LF in the 'name' state, reset the cursor and stay in
'name' rather than entering 'invalid'.

Problem:
`request()` and `notify()` are methods of the object returned by
`vim.lsp.rpc.start()`/`connect()`, but were rendered with module-level
helptags (`vim.lsp.rpc.request()`, `vim.lsp.rpc.notify()`) (erroneously
implying module functions that do not exist).

Solution:
Mark the wrappers `@private` and describe them on `vim.lsp.rpc.Client` instead.

Problem:
We perform validations after the request handler is called.
When these validations fail, `error()` and `assert()` will prevent the
subsequent code from running, meaning the server will never receive a response.

Solution:
Always respond to requests.

Problem:
PR #38340 prevented messages we receive with id:null from being
incorrectly classified as notifications, but caused us to ignore all
messages with id:null, including requests.

Solution:
Handle requests with id:null. When we receive a request, we only need to
respond based on the `method` and `param`.

(The original so-called `notification_received` in the test was actually
semantically `request_or_notification_received`.)