[ResponseOps] Migrate all usages of EuiPage*_Deprecated (#166188)

Fixes #161421

## Summary

As mentioned in the linked issue, I migrated all usages of
`EuiPage*_Deprecated` components listed below:


[x-pack/triggers_actions_ui](https://github.com/search?q=repo%3Aelastic%2Fkibana+%2FEuiPage%5Ba-zA-Z%5D%2B_Deprecated%2F+path%3A%2F%5Ex-pack%5C%2Fplugins%5C%2Ftriggers_actions_ui%2F&type=code)

[x-pack/examples/triggers_actions_ui_examples](https://github.com/search?q=repo%3Aelastic%2Fkibana+%2FEuiPage%5Ba-zA-Z%5D%2B_Deprecated%2F+path%3A%2F%5Ex-pack%5C%2Fexamples%5C%2Ftriggers_actions_ui_example%2F&type=code)

[x-pack/examples/alerting_example](https://github.com/search?q=repo%3Aelastic%2Fkibana+%2FEuiPage%5Ba-zA-Z%5D%2B_Deprecated%2F+path%3Ax-pack%2Fexamples%2Falerting_example&type=code)

[x-pack/test/functional_with_es_ssl/plugins/cases](https://github.com/search?q=repo%3Aelastic%2Fkibana+%2FEuiPage%5Ba-zA-Z%5D%2B_Deprecated%2F+path%3Ax-pack%2Ftest%2Ffunctional_with_es_ssl%2Fplugins%2Fcases&type=code)

The majority of these were in test environments and examples.

The only one actually in `x-pack/triggers_actions_ui` had to do with the
rule detail page. It looked basically the same after the change but a
`Pager` that was there became unnecessary. I removed it.

x-pack/examples/alerting_example/public/components/page.tsx

@@ -10,13 +10,12 @@ import { withRouter, RouteComponentProps } from 'react-router-dom';
 
 import {
   EuiPageBody,
-  EuiPageContent_Deprecated as EuiPageContent,
-  EuiPageContentBody_Deprecated as EuiPageContentBody,
   EuiPageHeader,
   EuiPageHeaderSection,
   EuiTitle,
   EuiBreadcrumbs,
   EuiSpacer,
+  EuiPageSection,
 } from '@elastic/eui';
 
 type PageProps = RouteComponentProps & {
@@ -54,9 +53,7 @@ export const Page = withRouter(({ title, crumb, children, isHome = false, histor
       </EuiPageHeader>
       <EuiBreadcrumbs responsive={false} breadcrumbs={breadcrumbs} />
       <EuiSpacer />
-      <EuiPageContent>
-        <EuiPageContentBody>{children}</EuiPageContentBody>
-      </EuiPageContent>
+      <EuiPageSection>{children}</EuiPageSection>
     </EuiPageBody>
   );
 });

x-pack/examples/triggers_actions_ui_example/public/components/page.tsx

@@ -8,16 +8,7 @@
 import React from 'react';
 import { useHistory } from 'react-router-dom';
 
-import {
-  EuiPageContent_Deprecated as EuiPageContent,
-  EuiPageContentBody_Deprecated as EuiPageContentBody,
-  EuiPageBody,
-  EuiPageHeader,
-  EuiPageHeaderSection,
-  EuiTitle,
-  EuiBreadcrumbs,
-  EuiSpacer,
-} from '@elastic/eui';
+import { EuiPageTemplate, EuiTitle, EuiBreadcrumbs } from '@elastic/eui';
 
 interface PageProps {
   title: string;
@@ -48,19 +39,14 @@ export const Page: React.FC<PageProps> = (props) => {
   }
 
   return (
-    <EuiPageBody>
-      <EuiPageHeader>
-        <EuiPageHeaderSection>
-          <EuiTitle size="l">
-            <h1>{title}</h1>
-          </EuiTitle>
-        </EuiPageHeaderSection>
-      </EuiPageHeader>
-      <EuiBreadcrumbs responsive={false} breadcrumbs={breadcrumbs} />
-      <EuiSpacer />
-      <EuiPageContent>
-        <EuiPageContentBody>{children}</EuiPageContentBody>
-      </EuiPageContent>
-    </EuiPageBody>
+    <EuiPageTemplate offset={0}>
+      <EuiPageTemplate.Header>
+        <EuiTitle size="l">
+          <h1>{title}</h1>
+        </EuiTitle>
+        <EuiBreadcrumbs responsive={false} breadcrumbs={breadcrumbs} />
+      </EuiPageTemplate.Header>
+      <EuiPageTemplate.Section>{children}</EuiPageTemplate.Section>
+    </EuiPageTemplate>
   );
 };

x-pack/plugins/triggers_actions_ui/public/application/sections/rule_details/components/rule_details.tsx

@@ -14,7 +14,7 @@ import {
   EuiFlexGroup,
   EuiFlexItem,
   EuiBadge,
-  EuiPageContentBody_Deprecated as EuiPageContentBody,
+  EuiPageSection,
   EuiCallOut,
   EuiSpacer,
   EuiButtonEmpty,
@@ -426,8 +426,7 @@ export const RuleDetails: React.FunctionComponent<RuleDetailsProps> = ({
           <ViewInApp rule={rule} />,
         ]}
       />
-      <EuiSpacer size="l" />
-      <EuiPageContentBody>
+      <EuiPageSection>
         {rule.enabled &&
         rule.executionStatus.error?.reason === RuleExecutionStatusErrorReasons.License ? (
           <EuiFlexGroup>
@@ -519,7 +518,7 @@ export const RuleDetails: React.FunctionComponent<RuleDetailsProps> = ({
             />
           </EuiFlexItem>
         </EuiFlexGroup>
-      </EuiPageContentBody>
+      </EuiPageSection>
     </>
   );
 };

x-pack/test/functional_with_es_ssl/plugins/cases/public/application.tsx

@@ -8,7 +8,7 @@
 import React from 'react';
 import ReactDOM from 'react-dom';
 import {
-  EuiPageTemplate_Deprecated as EuiPageTemplate,
+  EuiPageTemplate,
   EuiFlexGrid,
   EuiFlexItem,
   EuiPanel,