Follow-up: Add index modes summary and guidance to Manage data -> Data store overview

As a follow-up task, we need to add info about other index modes (vectordb_document and lookup) to the [data store](https://www.elastic.co/docs/manage-data/data-store) section.

## Context

On PR https://github.com/elastic/docs-content/pull/7594 we added a new overview page for columnar index mode and updated a few related pages to reference it. During review, we noted there are additional index modes (vectordb_document, lookup) and that the Data store section currently lacks guidance about how all the index modes relate and where to find details for each.

## Problem

The current data-store overview page is a general introduction to indices, mappings, and templates, but does not explain how index modes fit into the higher-level concepts. As a result:

- Readers who land on the data-store overview won't find a clear place that summarizes all available index modes and when to use them.
- The newly added columnar page links to the data-store section but the reverse isn't true for other index modes like vectordb_document and lookup, creating discoverability gaps.
- Some index-mode-specific behaviors (for example `_source` storage behavior and license restrictions for columnar) are mentioned on various pages but not consolidated or surfaced at the overview level.

## Request

Create follow-up documentation tasks to:

1. Add a short section in the Manage data -> Data store overview that lists available index modes (standard, logsdb, time_series, columnar, vectordb_document, lookup) with one-line guidance and links to reference pages.
2. Add a short explanatory paragraph that describes how index modes relate to mappings, templates, and `_source` behavior, with links to the relevant reference pages (including license implications where relevant).
3. Identify owner(s) and propose an initial plan for the content split (overview vs. per-mode details), and whether this should be an admin/dev collaboration.

## Notes and references

Relevant PR: https://github.com/elastic/docs-content/pull/7594
Relevant reference pages to link:
- index.mode setting: https://www.elastic.co/docs/reference/elasticsearch/index-settings/index-modules#index-mode-setting
- vectordb_document: https://www.elastic.co/docs/reference/elasticsearch/mapping-reference/dense-vector#dense-vector-vectordb-document-mode
- lookup/LOOKUP JOIN: https://www.elastic.co/docs/reference/query-languages/esql/esql-lookup-join
- Columnar reference PR: https://github.com/elastic/elasticsearch/pull/151739 (implementation details live here until back-merged into the reference)

Docs RICE prioritization

| Dimension | Score | Rationale |
|-----------|-------|-----------|
| R · Reach | 3 | 2,535 sessions/90d on the target overview page; discoverability improvement for the wider 30K-session section |
| I · Impact | 3 | Meaningful — fills a real navigation gap; no active harm but scattered index mode docs today |
| C · Confidence | 0.8 | Scope is mostly clear (add summary section + links); owner/collaboration plan still TBD |
| E · Effort | 0.5 | 2–3 days: write the summary section, cross-link to reference pages, coordinate |

**RICE = (3 × 3 × 0.8) / 0.5 = 14.4 → P2: Scheduled**
Scored: 2026-08-14

Start with the Manage data → Data store overview and review the referenced index.mode, dense-vector, ES|QL LOOKUP JOIN, and columnar materials, along with PR 7594. Map which guidance belongs on the overview versus the per-mode references and identify the owners or admin/dev contacts. Done means the content split and collaboration plan are agreed and the follow-up documentation tasks are clearly defined.

Written by the indexing model from the issue text.