fix: make ShutdownHandle a private field of LoginServer (#2396)

Folds the top-level `shutdown()` function into a method of
`ShutdownHandle` and then simply stores `ShutdownHandle` on
`LoginServer` since the two fields it contains were always being used
together, anyway.

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[//]: # (BEGIN SAPLING FOOTER)
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with [ReviewStack](https://reviewstack.dev/openai/codex/pull/2396).
* #2399
* #2398
* __->__ #2396
* #2395
* #2394
* #2393
* #2389

codex-rs/tui/src/onboarding/auth.rs

@@ -50,7 +50,7 @@ pub(crate) struct ContinueInBrowserState {
 impl Drop for ContinueInBrowserState {
     fn drop(&mut self) {
         if let Some(flag) = &self.shutdown_handle {
-            flag.cancel();
+            flag.shutdown();
         }
     }
 }