Add EDOT Browser SDK (elastic-otel-rum-js) to docs

[alexandra5000]

Summary

Adds the elastic-otel-rum-js repository integration ahead of the EDOT Browser tech preview release.

Changes

• Add elastic-otel-rum-js to cross_links in docset.yml
• Add EDOT Browser to the EDOT SDK list in the OpenTelemetry APM overview page
• Add Browser SDK to the EDOT SDKs troubleshooting index, linking directly to the troubleshooting page in the new repo

Related

• Add EDOT Browser SDK to EDOT SDKs documentation opentelemetry#568
• Add EDOT Browser (RUM) as applies_to product for preview badges docs-builder#2913
• Add EDOT Browser documentation elastic-otel-rum-js#36

Generative AI disclosure

1. Did you use a generative AI (GenAI) tool to assist in creating this contribution?

• Yes
• No

2. If you answered "Yes" to the previous question, please specify the tool(s) and model(s) used (e.g., Google Gemini, OpenAI ChatGPT-4, etc.).

Tool(s) and model(s) used: Claude Sonnet 4.6

[github-actions]

✅ Vale Linting Results

No issues found on modified lines!

---

The Vale linter checks documentation changes against the Elastic Docs style guide.

To use Vale locally or report issues, refer to Elastic style guide for Vale.