refactor: improve test isolation for Axios API logic (#13125)

* wip: commit progress on code split-up

* wip: commit more progress

* wip: finish initial version of class implementation

* chore: update all import paths to go through client instance

* fix: remove temp comments

* refactor: smoooooooosh the API

* refactor: update import setup for tests

site/e2e/global.setup.ts

@@ -1,5 +1,5 @@
 import { expect, test } from "@playwright/test";
-import { hasFirstUser } from "api/api";
+import { API } from "api/api";
 import { Language } from "pages/CreateUserPage/CreateUserForm";
 import { setupApiCalls } from "./api";
 import * as constants from "./constants";
@@ -9,7 +9,7 @@ import { storageState } from "./playwright.config";
 test("setup deployment", async ({ page }) => {
   await page.goto("/", { waitUntil: "domcontentloaded" });
   await setupApiCalls(page);
-  const exists = await hasFirstUser();
+  const exists = await API.hasFirstUser();
   // First user already exists, abort early. All tests execute this as a dependency,
   // if you run multiple tests in the UI, this will fail unless we check this.
   if (exists) {