Add corex library with resource-aware execution primitives

- Implement CI workflow for formatting, linting, testing, and documentation checks.
- Create publish workflow for automated publishing to crates.io.
- Add .gitignore to exclude build artifacts and editor files.
- Define Cargo.toml for corex and corex-core with dependencies and metadata.
- Add README.md files for corex and corex-core with usage instructions and licensing.
- Implement core execution primitives: spawn_io, compute, and spawn_bg with panic isolation.
- Establish global engine context for resource management based on logical CPU cores.
- Introduce error handling for compute panics.

crates/corex-core/src/bg.rs

@@ -0,0 +1,53 @@
+//! Bounded-concurrency background task execution.
+
+use tracing::Instrument;
+
+use crate::context::context;
+
+/// Spawns `future` as a background task once a concurrency permit is
+/// available, returning its [`tokio::task::JoinHandle`].
+///
+/// At most [`crate::context::EngineContext::bg_concurrency`] background
+/// tasks run at any one time; awaiting `spawn_bg` blocks the caller until a
+/// slot frees up, which is what provides the bound. A task's permit is held
+/// for the task's full lifetime and released automatically when it
+/// completes.
+///
+/// Panic isolation is provided by Tokio itself: a panicking background task
+/// cannot crash the runtime or any sibling task, and is surfaced to the
+/// caller as `Err(JoinError)` when the returned handle is awaited, exactly
+/// as with [`crate::io::spawn_io`].
+///
+/// # Panics
+///
+/// Panics if called outside the context of a running Tokio runtime.
+pub async fn spawn_bg<F>(future: F) -> tokio::task::JoinHandle<F::Output>
+where
+    F: std::future::Future + Send + 'static,
+    F::Output: Send + 'static,
+{
+    let permit = context()
+        .bg_semaphore
+        .acquire()
+        .await
+        .expect("corex: bg semaphore closed unexpectedly");
+    let span = tracing::info_span!("corex_bg_task");
+    tokio::spawn(
+        async move {
+            let _permit = permit;
+            future.await
+        }
+        .instrument(span),
+    )
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[tokio::test]
+    async fn spawn_bg_roundtrips_a_value() {
+        let handle = spawn_bg(async { 9u32 }).await;
+        assert_eq!(handle.await.unwrap(), 9);
+    }
+}