chore: rename ChatGpt -> Chatgpt in type names (#10244)

When using ChatGPT in names of types, we should be consistent, so this
renames some types with `ChatGpt` in the name to `Chatgpt`. From
https://rust-lang.github.io/api-guidelines/naming.html:

> In `UpperCamelCase`, acronyms and contractions of compound words count
as one word: use `Uuid` rather than `UUID`, `Usize` rather than `USize`
or `Stdin` rather than `StdIn`. In `snake_case`, acronyms and
contractions are lower-cased: `is_xid_start`.

This PR updates existing uses of `ChatGpt` and changes them to
`Chatgpt`. Though in all cases where it could affect the wire format, I
visually inspected that we don't change anything there. That said, this
_will_ change the codegen because it will affect the spelling of type
names.

For example, this renames `AuthMode::ChatGPT` to `AuthMode::Chatgpt` in
`app-server-protocol`, but the wire format is still `"chatgpt"`.

This PR also updates a number of types in `codex-rs/core/src/auth.rs`.

codex-rs/app-server-protocol/src/protocol/common.rs

@@ -30,7 +30,7 @@ pub enum AuthMode {
     /// OpenAI API key provided by the caller and stored by Codex.
     ApiKey,
     /// ChatGPT OAuth managed by Codex (tokens persisted and refreshed by Codex).
-    ChatGPT,
+    Chatgpt,
     /// [UNSTABLE] FOR OPENAI INTERNAL USE ONLY - DO NOT USE.
     ///
     /// ChatGPT auth tokens are supplied by an external host app and are only