How to Disable The New "Added By..." that's added into the Staff Notices Feature?

[Arkshine]

There is no setting solution for this. You can achieve this with some javascript, though:

In your theme or a new theme component, add the following in the JS tab:

import { apiInitializer } from "discourse/lib/api";
import { schedule } from "@ember/runloop";

export default apiInitializer((api) => {
  const current = api.getCurrentUser();
  if (!current || !current.staff) {
    return;
  }

  // Removes anything after the first paragraph 
  // containing the staff notice.
  api.decorateCookedElement((element, helper) => {
    const post = helper?.getModel();
    if (!post || !post.notice) {
      return;
    }

    schedule("afterRender", () => {
      const postNoticeMessage = document.querySelector(
        `article[data-post-id="${post.id}"] .post-notice-message`
      );

      if (postNoticeMessage) {
        postNoticeMessage.replaceWith(postNoticeMessage.firstChild);
      }
    });
  });
});

It should be good enough.