(DO NOT MERGE) Update machine auth docs after new additions

[SarahSoutoul]

🔎 Previews:

• https://clerk.com/docs/pr/ss-docs-10910/references/nextjs/auth
• https://clerk.com/docs/pr/ss-docs-10910/references/fastify/overview#get-auth
• https://clerk.com/docs/pr/ss-docs-10910/references/express/overview#get-auth
• https://clerk.com/docs/pr/ss-docs-10910/references/tanstack-react-start/get-auth
• https://clerk.com/docs/pr/ss-docs-10910/references/astro/locals#locals-auth-options
• https://clerk.com/docs/pr/ss-docs-10910/references/nuxt/overview#event-context-auth-options
• https://clerk.com/docs/pr/ss-docs-10910/references/react-router/get-auth

What does this solve?

This PR is waiting on this PR to be out

Linear: https://linear.app/clerk/issue/DOCS-10910/add-machine-auth-docs-for-astro-sdk

This was originally a ticket to add machine auth to the Astro SDK, as it's now supporting it. After working on it, I noticed a few discrepancies around machine auth for the other SDKs. Here are the things I noticed:

• Missing machine auth docs for Nuxt SDK
• Instances of machine_token instead of m2m_token, which is now the new name
• Parameters for most SDKs around machine auth weren't right according to JS repo changes
• secretKey parameter isn't needed anymore

What changed?

• Added machine auth details and code examples for Astro + Nuxt SDKs
• Changed all instances of machine_token to m2m_token
• Updated the parameters for most SDKs in terms of machine auth after consulting with @wobsoriano & looking at JS repo changes
• Removed secretKey parameter (not needed anymore)
• Added a partial for acceptsToken parameter given it's being used in a lot of places now, and contains lots of. text

Checklist

• I have clicked on "Files changed" and performed a thorough self-review
• All existing checks pass

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Project	Deployment	Preview	Updated (UTC)
clerk-docs	Ready	Preview	Sep 5, 2025 6:49pm

[SarahSoutoul]

Thanks for review/ feedback @alexisintech - made all the changes here: Changes after feedback

[wobsoriano]

thanks!