[Infra] Send Host View Total Host Count Retrieved event on every query submission in hosts inventory (#202691)

## Summary

Fixes https://github.com/elastic/kibana/issues/202441

This PR reintroduces the `Host View Total Host Count Retrieved` event,
which was unintentionally removed in the past. It has been added back to
the same position in the code as previously

|Scenario|Event|
|-|-|
|Page load|![Screenshot 2024-12-03 at 12 37
28](https://github.com/user-attachments/assets/8a12d713-219b-4c1f-a08e-7b475634b4fc)|
|Query|![Screenshot 2024-12-03 at 12 40
12](https://github.com/user-attachments/assets/501a8a81-b0b0-46a6-a470-dceeba791c01)|
|Filter|![Screenshot 2024-12-03 at 12 40
56](https://github.com/user-attachments/assets/586f2176-b05b-4571-b3d8-f3f9cb803249)|

x-pack/plugins/observability_solution/infra/public/pages/metrics/hosts/hooks/use_host_count.test.ts

@@ -0,0 +1,144 @@
+/*
+ * 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; you may not use this file except in compliance with the Elastic License
+ * 2.0.
+ */
+
+import { renderHook } from '@testing-library/react';
+import { useFetcher } from '../../../../hooks/use_fetcher';
+import { useKibanaContextForPlugin } from '../../../../hooks/use_kibana';
+import * as useKibanaContextForPluginHook from '../../../../hooks/use_kibana';
+import * as useUnifiedSearchHooks from './use_unified_search';
+import { useHostCount } from './use_host_count';
+
+jest.mock('../../../../hooks/use_fetcher');
+jest.mock('../../../../hooks/use_kibana');
+jest.mock('./use_unified_search');
+
+describe('useHostCount', () => {
+  const useKibanaContextForPluginMock = useKibanaContextForPlugin as jest.MockedFunction<
+    typeof useKibanaContextForPlugin
+  >;
+
+  const telemetryMock = { reportHostsViewTotalHostCountRetrieved: jest.fn() };
+
+  useKibanaContextForPluginMock.mockReturnValue({
+    services: { telemetry: telemetryMock },
+  } as unknown as ReturnType<typeof useKibanaContextForPluginHook.useKibanaContextForPlugin>);
+
+  const useUnifiedSearchContextMock =
+    useUnifiedSearchHooks.useUnifiedSearchContext as jest.MockedFunction<
+      typeof useUnifiedSearchHooks.useUnifiedSearchContext
+    >;
+
+  const mockUseUnifiedContext = (searchCriteria: any) => {
+    useUnifiedSearchContextMock.mockReturnValue({
+      buildQuery: jest.fn(() => 'query'),
+      parsedDateRange: { from: '', to: '' },
+      searchCriteria,
+    } as unknown as ReturnType<typeof useUnifiedSearchHooks.useUnifiedSearchContext>);
+  };
+
+  describe('when data is fetched', () => {
+    const fetcherDataMock = { count: 10 };
+
+    beforeAll(() => {
+      (useFetcher as jest.Mock).mockReturnValue({
+        data: fetcherDataMock,
+        status: 'success',
+        error: null,
+      });
+    });
+
+    afterEach(() => {
+      jest.clearAllMocks();
+    });
+
+    describe('and there is no filters or query applied', () => {
+      it('should call reportHostsViewTotalHostCountRetrieved with the correct data', async () => {
+        mockUseUnifiedContext({
+          query: { query: null },
+          filters: [],
+          panelFilters: [],
+        });
+
+        await renderHook(() => useHostCount());
+
+        expect(telemetryMock.reportHostsViewTotalHostCountRetrieved).toHaveBeenCalledWith({
+          total: fetcherDataMock.count,
+          with_query: false,
+          with_filters: false,
+        });
+      });
+    });
+
+    describe('and query is applied', () => {
+      it('should call reportHostsViewTotalHostCountRetrieved with the correct data', async () => {
+        mockUseUnifiedContext({ query: { query: 'test' }, filters: [], panelFilters: [] });
+
+        await renderHook(() => useHostCount());
+
+        expect(telemetryMock.reportHostsViewTotalHostCountRetrieved).toHaveBeenCalledWith({
+          total: fetcherDataMock.count,
+          with_query: true,
+          with_filters: false,
+        });
+      });
+    });
+
+    describe('and filters are applied', () => {
+      it('should call reportHostsViewTotalHostCountRetrieved with the correct data', async () => {
+        mockUseUnifiedContext({
+          query: { query: null },
+          filters: [{ filter: 'filter' }],
+          panelFilters: [],
+        });
+
+        await renderHook(() => useHostCount());
+
+        expect(telemetryMock.reportHostsViewTotalHostCountRetrieved).toHaveBeenCalledWith({
+          total: fetcherDataMock.count,
+          with_query: false,
+          with_filters: true,
+        });
+      });
+    });
+
+    describe('and panel filters are applied', () => {
+      it('should call reportHostsViewTotalHostCountRetrieved with the correct data', async () => {
+        mockUseUnifiedContext({
+          query: { query: null },
+          filters: [{ filter: 'filter' }],
+          panelFilters: [{ filter: 'filter' }],
+        });
+
+        await renderHook(() => useHostCount());
+
+        expect(telemetryMock.reportHostsViewTotalHostCountRetrieved).toHaveBeenCalledWith({
+          total: fetcherDataMock.count,
+          with_query: false,
+          with_filters: true,
+        });
+      });
+    });
+  });
+
+  describe('when data is fetched with error', () => {
+    beforeAll(() => {
+      (useFetcher as jest.Mock).mockReturnValue({
+        data: {},
+        status: 'error',
+        error: 'error',
+      });
+    });
+
+    it('should NOT call reportHostsViewTotalHostCountRetrieved ', async () => {
+      mockUseUnifiedContext(null);
+
+      await renderHook(() => useHostCount());
+
+      expect(telemetryMock.reportHostsViewTotalHostCountRetrieved).not.toHaveBeenCalled();
+    });
+  });
+});

x-pack/plugins/observability_solution/infra/public/pages/metrics/hosts/hooks/use_host_count.ts

@@ -7,13 +7,16 @@
 
 import createContainer from 'constate';
 import { decodeOrThrow } from '@kbn/io-ts-utils';
-import { useMemo } from 'react';
+import { useMemo, useEffect } from 'react';
+import { useKibanaContextForPlugin } from '../../../../hooks/use_kibana';
 import { GetInfraAssetCountResponsePayloadRT } from '../../../../../common/http_api';
 import { isPending, useFetcher } from '../../../../hooks/use_fetcher';
 import { useUnifiedSearchContext } from './use_unified_search';
 
 export const useHostCount = () => {
-  const { buildQuery, parsedDateRange } = useUnifiedSearchContext();
+  const { buildQuery, parsedDateRange, searchCriteria } = useUnifiedSearchContext();
+  const { services } = useKibanaContextForPlugin();
+  const { telemetry } = services;
 
   const payload = useMemo(
     () =>
@@ -37,6 +40,16 @@ export const useHostCount = () => {
     [payload]
   );
 
+  useEffect(() => {
+    if (data && !error) {
+      telemetry.reportHostsViewTotalHostCountRetrieved({
+        total: data.count ?? 0,
+        with_query: !!searchCriteria.query.query,
+        with_filters: searchCriteria.filters.length > 0 || searchCriteria.panelFilters.length > 0,
+      });
+    }
+  }, [data, error, payload, searchCriteria, telemetry]);
+
   return {
     errors: error,
     loading: isPending(status),