Remove the deprecated Claude subscription login path and restore a green Rust workspace

ROADMAP #37 was still open even though several earlier backlog items were
already closed. This change removes the local login/logout surface, stops
startup auth resolution from treating saved OAuth credentials as a supported
path, and updates diagnostics/help to point users at ANTHROPIC_API_KEY or
ANTHROPIC_AUTH_TOKEN only.

While proving the change with the user-requested workspace gates, clippy
surfaced additional pre-existing warning failures across the Rust workspace.
Those were cleaned up in-place so the required `cargo fmt`, `cargo clippy
--workspace --all-targets -- -D warnings`, and `cargo test --workspace`
sequence now passes end to end.

Constraint: User explicitly required full-workspace fmt/clippy/test before commit/push
Constraint: Existing dirty leader worktree had to be stashed before attempted OMX team worktree launch
Rejected: Keep login/logout but hide them from help | left unsupported auth flow and saved OAuth fallback intact
Rejected: Stop after ROADMAP #37 targeted tests | did not satisfy required full-workspace verification gate
Confidence: medium
Scope-risk: moderate
Reversibility: clean
Directive: Do not reintroduce saved OAuth as a silent Anthropic startup fallback without an explicit supported auth policy
Tested: cargo fmt --all --check; cargo clippy --workspace --all-targets -- -D warnings; cargo test --workspace
Not-tested: Remote push effects beyond origin/main update

rust/crates/runtime/src/session.rs

@@ -1467,12 +1467,8 @@ mod tests {
 /// Called by external consumers (e.g. clawhip) to enumerate sessions for a CWD.
 #[allow(dead_code)]
 pub fn workspace_sessions_dir(cwd: &std::path::Path) -> Result<std::path::PathBuf, SessionError> {
-    let store = crate::session_control::SessionStore::from_cwd(cwd).map_err(|e| {
-        SessionError::Io(std::io::Error::new(
-            std::io::ErrorKind::Other,
-            e.to_string(),
-        ))
-    })?;
+    let store = crate::session_control::SessionStore::from_cwd(cwd)
+        .map_err(|e| SessionError::Io(std::io::Error::other(e.to_string())))?;
     Ok(store.sessions_dir().to_path_buf())
 }
 
@@ -1489,8 +1485,7 @@ mod workspace_sessions_dir_tests {
         let result = workspace_sessions_dir(&tmp);
         assert!(
             result.is_ok(),
-            "workspace_sessions_dir should succeed for a valid CWD, got: {:?}",
-            result
+            "workspace_sessions_dir should succeed for a valid CWD, got: {result:?}"
         );
         let dir = result.unwrap();
         // The returned path should be non-empty and end with a hash component