docs: port ClickStack nurture flow / OTel collector updates

[mintlify]

Summary

Ports ClickHouse/clickhouse-docs#6335 (ClickStack - Nurture flow - Otel collector) to the Mintlify docs.

Changes

• Removed BetaBadge and the "Beta feature" note from products/clickstack/deployment/managed.mdx and products/clickstack/getting-started/managed.mdx (Managed ClickStack is now GA).
• Added new "Synthetic data with otelgen" entry to the example datasets index and created products/clickstack/example-datasets/otelgen.mdx. Slug preserved as /use-cases/observability/clickstack/getting-started/otelgen.
• Created products/clickstack/managed-onboarding/setting-up-your-opentelemetry-collector.mdx (kept unlisted: true as in source — not added to navigation). Slug preserved as /use-cases/observability/clickstack/setting-up-your-opentelemetry-collector.
• Copied 4 new images: clickstack-cloud-v2.png, clickstack-search.png, clickstack-start-exploring.png, clickstack-start-ingestion.png.
• Added otelgen to products/clickstack/navigation.json under Sample datasets.

Conversion notes / ambiguities

• Docusaurus <VerticalStepper headerLevel="h3"> was converted to Mintlify <Steps> / <Step>.
• Docusaurus <Tabs groupId="..."> was converted to plain Mintlify <Tabs> / <Tab title="..."> (Mintlify Tabs don't support shared groupId state).
• :::note blocks were converted to Mintlify <Note> components.
• Internal links that referenced /use-cases/observability/clickstack/ingesting-data/otel-collector#... were retargeted to the equivalent Mintlify route /products/clickstack/ingesting-data/collector#....
• The Docusaurus change to src/theme/DocItem/TOC/Desktop/index.js is Docusaurus-only theming and was not ported.
• The new setting-up-your-opentelemetry-collector page is marked unlisted: true upstream (intended to be reachable from the ClickStack UI rather than nav); replicated by not adding it to navigation.json. Flagging in case it should also be linked from the deployment/managed page.

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Note

Low Risk
Documentation-only changes (copy, nav, and new guides); no application or ingestion runtime code.

Overview
Ports the ClickStack nurture / OpenTelemetry collector documentation into Mintlify and treats Managed ClickStack as GA on the main getting-started and deployment pages.

Managed ClickStack GA: Removes the BetaBadge component and the beta callout from products/clickstack/getting-started/managed.mdx and products/clickstack/deployment/managed.mdx.

Synthetic telemetry: Adds products/clickstack/example-datasets/otelgen.mdx with Managed vs Open Source tabs for installing otelgen, sending OTLP logs/traces/metrics to the collector (including optional OTLP_AUTH_TOKEN / API key headers), and verifying data in the UI. Lists the page on the sample datasets index and in products/clickstack/navigation.json.

Collector onboarding: Adds products/clickstack/managed-onboarding/setting-up-your-opentelemetry-collector.mdx (unlisted: true, not in nav) with steps to gather Cloud credentials, create hyperdx_ingest, run clickhouse/clickstack-otel-collector, verify with otelgen, and confirm ingestion in the ClickStack UI (new screenshots referenced in the PR description).

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