DOC-359 (hotfix): Add lstk docs to Azure docs

[quetzalliwrites]

Summary

• Add the lstk CLI reference doc (src/content/docs/azure/developer-tools/lstk.mdx), mirroring the existing AWS and Snowflake copies.
• Add a new "Developer Tools" sidebar section for Azure docs (autogenerated from azure/developer-tools), matching the AWS naming convention.
• Repoint the auth-token prerequisite link to the Azure equivalent (/azure/getting-started/auth-token/#managing-your-license); the Docker Compose install guide, corporate proxy FAQ, and Get Help links still point to the AWS docs since Azure has no equivalent pages for those.

Linear: https://linear.app/localstack/issue/DOC-359/add-lstk-docs-to-azure-docs

Test plan

• astro build completes successfully
• Page renders at /azure/developer-tools/lstk/
• "lstk CLI" appears under the new "Developer Tools" section in the Azure sidebar
• starlight-links-validator reports all internal links valid

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[mmaureenliu]

Thanks!

No problem with this PR. Just two questions:

• Will the lstk doc automatically syncs with the AWS lstk doc update?
• In AWS docs, the CLI doc is under "Running LocalStack" within the "Developer Tools" section. Is the plan to eventually mirror that structure in Azure when more dev tools become available?

[quetzalliwrites]

Good questions, @mmaureenliu! ty

1. We are building re-usable components that will be used across all product lines. This means that the same re-usable lstk component will be the one that automatically updates, thus keeping all product lines in sync.
2. Yes, exactly, you got it. As we add more documentation around dev tools for the Azure product line, the information architecture is mirrored across product lines as applicable. (right now, it's a bad user experience to add 2 levels of directories when only 1 doc is added)