fix: strip /agent/<name>/ via rewrite in named location

nginx forbids a URI part on proxy_pass inside named locations, so the
split-mode `@<name>_dynamic` fallback (introduced when the gateway
started serving static dist directly) failed config-test with:

  "proxy_pass" cannot have URI part in location given by regular
  expression, or inside named location

Render two upstream forms: prefix locations keep the trailing slash so
nginx auto-strips the location prefix; the named-location path strips
`/agent/<name>/` via `rewrite ... break` and uses a bare upstream.

hive-c0re/src/gateway_nginx.rs

@@ -76,13 +76,22 @@ fn render(names: &[String], frontend_dir: Option<&str>) -> String {
     );
     for name in names {
         let port = lifecycle::agent_web_port(name);
-        let upstream = if agent_sockets::ready_marker_for(name).exists() {
+        // Two upstream forms because named locations (split mode's
-            format!(
+        // `@<name>_dynamic`) forbid a URI part on `proxy_pass`. The
-                "http://unix:{}:/",
+        // legacy prefix-location path keeps the trailing `/` so nginx
-                agent_sockets::socket_path_for(name).display()
+        // strips `/agent/<name>/` automatically; the named-location
+        // path strips the prefix via `rewrite` and uses a bare upstream.
+        let (upstream_prefix, upstream_bare) = if agent_sockets::ready_marker_for(name).exists() {
+            let sock = agent_sockets::socket_path_for(name).display().to_string();
+            (
+                format!("http://unix:{sock}:/"),
+                format!("http://unix:{sock}:"),
             )
         } else {
-            format!("http://127.0.0.1:{port}/")
+            (
+                format!("http://127.0.0.1:{port}/"),
+                format!("http://127.0.0.1:{port}"),
+            )
         };
 
         if let Some(frontend) = frontend_dir {
@@ -124,7 +133,8 @@ fn render(names: &[String], frontend_dir: Option<&str>) -> String {
                  }}\n\
                  \nlocation @{name}_dynamic {{\n\
                  {PROXY_HEADER_BLOCK}\n\
-                 \n    proxy_pass {upstream};\n\
+                 \n    rewrite ^/agent/{name}/(.*)$ /$1 break;\n\
+                 \n    proxy_pass {upstream_bare};\n\
                  \n    proxy_set_header X-Forwarded-Prefix /agent/{name};\n\
                  \n    proxy_buffering off;\n\
                  \n    proxy_read_timeout 1d;\n\
@@ -138,7 +148,7 @@ fn render(names: &[String], frontend_dir: Option<&str>) -> String {
                 out,
                 "\nlocation /agent/{name}/ {{\n\
                  {PROXY_HEADER_BLOCK}\n\
-                 \n    proxy_pass {upstream};\n\
+                 \n    proxy_pass {upstream_prefix};\n\
                  \n    proxy_set_header X-Forwarded-Prefix /agent/{name};\n\
                  \n    proxy_buffering off;\n\
                  \n    proxy_read_timeout 1d;\n\
@@ -381,6 +391,40 @@ mod tests {
         assert!(body.contains("__hive_agent_unreachable"));
     }
 
+    #[test]
+    fn split_mode_named_location_strips_prefix_without_uri_part() {
+        // Named locations forbid a URI part on proxy_pass — nginx rejects
+        // `proxy_pass http://host/` inside `location @name`. Must use
+        // bare upstream (no trailing `/` or path) plus a `rewrite` to
+        // strip the /agent/<name>/ prefix.
+        let names = vec!["iris".to_owned()];
+        let body = render(&names, Some(FAKE_FRONTEND));
+        assert!(
+            body.contains("rewrite ^/agent/iris/(.*)$ /$1 break;"),
+            "expected prefix-strip rewrite, got:\n{body}"
+        );
+        // The named-location proxy_pass must have no URI part (no
+        // trailing slash or path). Extract the `@iris_dynamic { ... }`
+        // block and check every proxy_pass directive in it.
+        let block_start = body.find("location @iris_dynamic {").expect("named location");
+        let block = &body[block_start..];
+        let block_end = block.find("\n}\n").expect("block close");
+        let block = &block[..block_end];
+        for line in block.lines() {
+            let line = line.trim();
+            if let Some(rest) = line.strip_prefix("proxy_pass ") {
+                let target = rest.trim_end_matches(';');
+                // No URI part means: TCP form `http://host:port` (no
+                // trailing `/`), UDS form `http://unix:/path:` (trailing
+                // colon, nothing after). Both cases: must not end in `/`.
+                assert!(
+                    !target.ends_with('/'),
+                    "named-location proxy_pass must have no URI part, got: {target}"
+                );
+            }
+        }
+    }
+
     #[test]
     fn split_mode_includes_manager() {
         let names: Vec<String> = [MANAGER_NAME, "iris"]