build: upgrade all preview-server JS dependencies to latest versions (#38736)

This commit upgrades all dependencies in `aio/aio-builds-setup/scripts-js/`
to latest versions and also includes all necessary code changes to
ensure the tests are passing with the new dependency versions.

In particular:
- We ensure `nock`'s `Scope#done()` is not called before receiving a
  response to account for a breaking change introduced in
  nock/nock#1960.
- The use of `nock`'s `Scope#log()` method was removed, because the
  method is no longer available since nock/nock#1966. See
  https://github.com/nock/nock#debugging for more info on debugging
  failed matches.

See also
e23ba31b13/migration_guides/migrating_to_13.md
for more info on migrating from `nock` v12 to v13.

PR Close #38736

aio/aio-builds-setup/dockerbuild/scripts-js/test/common/github-api.spec.ts

@@ -214,23 +214,24 @@ describe('GithubApi', () => {
     });
 
 
-    it('should call \'https.request()\' with the correct options', () => {
+    it('should call \'https.request()\' with the correct options', async () => {
       const requestHandler = nock('https://api.github.com')
         .intercept('/path', 'method')
         .reply(200);
 
-      (api as any).request('method', '/path');
+      await (api as any).request('method', '/path');
       requestHandler.done();
     });
 
 
-    it('should add the \'Authorization\' header containing the \'githubToken\'', () => {
+    it('should add the \'Authorization\' header containing the \'githubToken\'', async () => {
       const requestHandler = nock('https://api.github.com')
         .intercept('/path', 'method', undefined, {
           reqheaders: {Authorization: 'token 12345'},
         })
         .reply(200);
-      (api as any).request('method', '/path');
+
+      await (api as any).request('method', '/path');
       requestHandler.done();
     });
 
@@ -244,12 +245,13 @@ describe('GithubApi', () => {
     });
 
 
-    it('should \'JSON.stringify\' and send the data along with the request', () => {
+    it('should \'JSON.stringify\' and send the data along with the request', async () => {
       const data = {key: 'value'};
       const requestHandler = nock('https://api.github.com')
         .intercept('/path', 'method', JSON.stringify(data))
         .reply(200);
-      (api as any).request('method', '/path', data);
+
+      await (api as any).request('method', '/path', data);
       requestHandler.done();
     });