collab: Make the StripeBilling object long-lived (#19090)

This PR makes the `StripeBilling` object long-lived so that we can make
better use of the cached data on it.

We now hold it on the `AppState` and spawn a background task to
initialize the cache on startup.

Release Notes:

- N/A

Co-authored-by: Richard <richard@zed.dev>

crates/collab/src/tests/test_server.rs

@@ -639,6 +639,7 @@ impl TestServer {
             live_kit_client: Some(Arc::new(live_kit_test_server.create_api_client())),
             blob_store_client: None,
             stripe_client: None,
+            stripe_billing: None,
             rate_limiter: Arc::new(RateLimiter::new(test_db.db().clone())),
             executor,
             clickhouse_client: None,