[DPE-9412] docs: Us spelling update

[izmalk]

Description of issue or feature:

This PR is for adopting US spelling instead of UK spelling.

Solution:

Fix all detected issues.
Check with a custom-made spellchecker locally with a US-English dictionary.
We do not apply a custom spellchecker here but rather work on it for the upstream.

How was this change tested?

• Manually
• Unit tests
• Integration tests

Checked with copilot.
Tested with Vale with US-specific dictionary.

Checklist

• I have added or updated any relevant documentation.
• I have cleaned any remaining cloud resources from my accounts.

[Copilot]

Pull request overview

This PR updates documentation wording to consistently use US English spellings across several pages in the docs set.

Changes:

• Update UK spellings to US spellings (e.g., fulfils→fulfills, centralises→centralizes, organised→organized, summarised→summarized).
• Replace “Amongst” with “Among” for US usage.

Reviewed changes

Copilot reviewed 5 out of 5 changed files in this pull request and generated 1 comment.

Show a summary per file

File	Description
docs/tutorial/index.md	US spelling update in the tutorial prerequisites list.
docs/tutorial/3-enable-encryption.md	US spelling update in TLS/encryption tutorial text.
docs/index.md	US spelling update in a top-level documentation section heading.
docs/how-to/deploy/launch-a-large-deployment.md	US wording update in the “node roles” section intro.
docs/explanation/index.md	US spelling update in the explanation index intro text.

Comments suppressed due to low confidence (1)

docs/how-to/deploy/launch-a-large-deployment.md:21

• The bullet list under node roles appears to be unintentionally split into multiple top-level bullets (e.g., - creating and deleting indices... looks like a continuation of the cluster_manager description). Consider wrapping those lines as part of the same bullet (indent continuation lines) or making them nested sub-bullets for clearer structure.

Among the [multiple roles](https://opensearch.org/docs/latest/tuning-your-cluster/) supported by
OpenSearch, two notable roles are especially crucial for a successful cluster formation:

- `cluster_manager`: assigned to nodes responsible for handling cluster-wide operations such as
- creating and deleting indices, managing shards, and rebalancing data across the cluster.

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