fix(docker): harden frontend runtime config

frontend/src/api/runtime-config.test.ts

@@ -1,6 +1,6 @@
 import { describe, expect, it } from "vitest";
 
-import { backendBaseUrl, resolveBackendUrl } from "./runtime-config";
+import { backendBaseUrl, joinBackendPath, resolveBackendUrl } from "./runtime-config";
 
 describe("resolveBackendUrl", () => {
   it("uses the runtime-injected backend URL", () => {
@@ -15,3 +15,16 @@ describe("resolveBackendUrl", () => {
     expect(backendBaseUrl).toBe(import.meta.env.VITE_BACKEND_URL ?? "http://localhost:8787");
   });
 });
+
+describe("joinBackendPath", () => {
+  it.each([
+    ["", "/sessions/s1", "/sessions/s1"],
+    ["/", "/sessions/s1", "/sessions/s1"],
+    ["/api", "/sessions/s1", "/api/sessions/s1"],
+    ["/api/", "/sessions/s1", "/api/sessions/s1"],
+    ["https://example.test/api", "/sessions/s1", "https://example.test/api/sessions/s1"],
+    ["https://example.test/api/", "sessions/s1", "https://example.test/api/sessions/s1"],
+  ])("joins base %j and path %j", (base, path, expected) => {
+    expect(joinBackendPath(base, path)).toBe(expected);
+  });
+});