[Dashboard] Fix share dashboard iframe embed code incorrectly (#194366)

## Summary

Fixes [#192980](#193447)

Maybe related pr: #179037 

After fix it, having an URL that is like this:
```
?embed=true&_g=(refreshInterval%3A(pause%3A!t%2Cvalue%3A60000)%2Ctime%3A(from%3Anow-15m%2Cto%3Anow))&hide-filter-bar=true
```

**Screenshot**
<img width="1918" alt="image"
src="https://github.com/user-attachments/assets/de069fdb-895e-479a-b868-891bbb55594e">

---------

Co-authored-by: Elastic Machine <[email protected]>
Co-authored-by: Tim Sullivan <[email protected]>

src/plugins/share/public/components/context/index.tsx

@@ -29,7 +29,6 @@ export interface IShareContext extends ShareContext {
   anonymousAccess?: AnonymousAccessServiceContract;
   urlService: BrowserUrlService;
   snapshotShareWarning?: string;
-  isEmbedded: boolean;
   theme: ThemeServiceSetup;
   i18n: I18nStart;
   publicAPIEnabled?: boolean;

src/plugins/share/public/components/share_tabs.test.tsx

@@ -53,7 +53,6 @@ const mockShareContext = {
   allowShortUrl: true,
   anonymousAccess: { getCapabilities: jest.fn(), getState: jest.fn() },
   urlService: service,
-  isEmbedded: true,
   theme: themeServiceMock.createStartContract(),
   objectTypeMeta: { title: 'title' },
   objectType: 'type',

src/plugins/share/public/components/tabs/embed/embed_content.test.tsx

@@ -0,0 +1,56 @@
+/*
+ * Copyright Elasticsearch B.V. and/or licensed to Elasticsearch B.V. under one
+ * or more contributor license agreements. Licensed under the "Elastic License
+ * 2.0", the "GNU Affero General Public License v3.0 only", and the "Server Side
+ * Public License v 1"; you may not use this file except in compliance with, at
+ * your election, the "Elastic License 2.0", the "GNU Affero General Public
+ * License v3.0 only", or the "Server Side Public License, v 1".
+ */
+
+import { mountWithIntl } from '@kbn/test-jest-helpers';
+import { EmbedContent } from './embed_content';
+import React from 'react';
+import { ReactWrapper } from 'enzyme';
+
+describe('Share modal embed content tab', () => {
+  describe('share url embedded', () => {
+    let component: ReactWrapper;
+
+    beforeEach(() => {
+      component = mountWithIntl(
+        <EmbedContent
+          objectType="dashboard"
+          setIsNotSaved={() => jest.fn()}
+          shareableUrl="/home#/"
+        />
+      );
+    });
+
+    it('works for simple url', async () => {
+      component.setProps({ shareableUrl: 'http://localhost:5601/app/home#/' });
+      component.update();
+
+      const shareUrl = component
+        .find('button[data-test-subj="copyEmbedUrlButton"]')
+        .prop('data-share-url');
+      expect(shareUrl).toBe(
+        '<iframe src="http://localhost:5601/app/home#/?embed=true&_g=" height="600" width="800"></iframe>'
+      );
+    });
+
+    it('works if the url has a query string', async () => {
+      component.setProps({
+        shareableUrl:
+          'http://localhost:5601/app/dashboards#/create?_g=(refreshInterval%3A(pause%3A!t%2Cvalue%3A60000)%2Ctime%3A(from%3Anow-15m%2Cto%3Anow))',
+      });
+      component.update();
+
+      const shareUrl = component
+        .find('button[data-test-subj="copyEmbedUrlButton"]')
+        .prop('data-share-url');
+      expect(shareUrl).toBe(
+        '<iframe src="http://localhost:5601/app/dashboards#/create?embed=true&_g=(refreshInterval%3A(pause%3A!t%2Cvalue%3A60000)%2Ctime%3A(from%3Anow-15m%2Cto%3Anow))" height="600" width="800"></iframe>'
+      );
+    });
+  });
+});

src/plugins/share/public/components/tabs/embed/embed_content.tsx

@@ -30,7 +30,6 @@ type EmbedProps = Pick<
   | 'shareableUrlLocatorParams'
   | 'shareableUrlForSavedObject'
   | 'shareableUrl'
-  | 'isEmbedded'
   | 'embedUrlParamExtensions'
   | 'objectType'
 > & {
@@ -52,7 +51,6 @@ export const EmbedContent = ({
   embedUrlParamExtensions: urlParamExtensions,
   shareableUrlForSavedObject,
   shareableUrl,
-  isEmbedded,
   objectType,
   setIsNotSaved,
 }: EmbedProps) => {
@@ -69,6 +67,17 @@ export const EmbedContent = ({
     if (objectType !== 'dashboard') setIsNotSaved();
   }, [url, setIsNotSaved, objectType]);
 
+  const makeUrlEmbeddable = useCallback((tempUrl: string): string => {
+    const embedParam = '?embed=true';
+    const urlHasQueryString = tempUrl.indexOf('?') !== -1;
+
+    if (urlHasQueryString) {
+      return tempUrl.replace('?', `${embedParam}&`);
+    }
+
+    return `${tempUrl}${embedParam}`;
+  }, []);
+
   const getUrlParamExtensions = useCallback(
     (tempUrl: string): string => {
       return urlParams
@@ -90,10 +99,11 @@ export const EmbedContent = ({
 
   const updateUrlParams = useCallback(
     (tempUrl: string) => {
+      tempUrl = makeUrlEmbeddable(tempUrl);
       tempUrl = urlParams ? getUrlParamExtensions(tempUrl) : tempUrl;
       return tempUrl;
     },
-    [getUrlParamExtensions, urlParams]
+    [makeUrlEmbeddable, getUrlParamExtensions, urlParams]
   );
 
   const getSnapshotUrl = useCallback(
@@ -180,16 +190,14 @@ export const EmbedContent = ({
       tempUrl = addUrlAnonymousAccessParameters(tempUrl!);
     }
 
-    if (isEmbedded) {
-      tempUrl = makeIframeTag(tempUrl!);
-    }
+    tempUrl = makeIframeTag(tempUrl!);
+
     setUrl(tempUrl!);
   }, [
     addUrlAnonymousAccessParameters,
     exportUrlAs,
     getSavedObjectUrl,
     getSnapshotUrl,
-    isEmbedded,
     shortUrlCache,
     useShortUrl,
   ]);

src/plugins/share/public/components/tabs/embed/index.tsx

@@ -38,14 +38,8 @@ const embedTabReducer: IEmbedTab['reducer'] = (state = { url: '', isNotSaved: fa
 };
 
 const EmbedTabContent: NonNullable<IEmbedTab['content']> = ({ state, dispatch }) => {
-  const {
-    embedUrlParamExtensions,
-    shareableUrlForSavedObject,
-    shareableUrl,
-    isEmbedded,
-    objectType,
-    isDirty,
-  } = useShareTabsContext()!;
+  const { embedUrlParamExtensions, shareableUrlForSavedObject, shareableUrl, objectType, isDirty } =
+    useShareTabsContext()!;
 
   const setIsNotSaved = useCallback(() => {
     dispatch({
@@ -60,7 +54,6 @@ const EmbedTabContent: NonNullable<IEmbedTab['content']> = ({ state, dispatch })
         embedUrlParamExtensions,
         shareableUrlForSavedObject,
         shareableUrl,
-        isEmbedded,
         objectType,
         isNotSaved: state?.isNotSaved,
         setIsNotSaved,

src/plugins/share/public/services/share_menu_manager.tsx

@@ -129,7 +129,6 @@ export class ShareMenuManager {
           snapshotShareWarning,
           disabledShareUrl,
           isDirty,
-          isEmbedded: allowEmbed,
           shareMenuItems: menuItems,
           toasts,
           onClose: () => {