refactor(pageserver): refactor pageserver router state creation (#5165)

Fixes #3894 by:
- Refactor the pageserver router creation flow
- Create the router state in `pageserver/src/bin/pageserver.rs`

pageserver/src/bin/pageserver.rs

@@ -477,16 +477,19 @@ fn start_pageserver(
     {
         let _rt_guard = MGMT_REQUEST_RUNTIME.enter();
 
-        let router = http::make_router(
-            conf,
-            launch_ts,
-            http_auth,
-            broker_client.clone(),
-            remote_storage,
-            disk_usage_eviction_state,
-        )?
-        .build()
-        .map_err(|err| anyhow!(err))?;
+        let router_state = Arc::new(
+            http::routes::State::new(
+                conf,
+                http_auth.clone(),
+                remote_storage,
+                broker_client.clone(),
+                disk_usage_eviction_state,
+            )
+            .context("Failed to initialize router state")?,
+        );
+        let router = http::make_router(router_state, launch_ts, http_auth.clone())?
+            .build()
+            .map_err(|err| anyhow!(err))?;
         let service = utils::http::RouterService::new(router).unwrap();
         let server = hyper::Server::from_tcp(http_listener)?
             .serve(service)