docs: restructure Deploy section around surface × access mode

[Him188]

Summary

The old Deploy overview presented a four-step "channel ladder" (widget → public → authenticated → phone) that conflated two orthogonal axes — clicking 3. Authenticated sessions landed on a page titled Authentication that re-explained both access modes, including a Public agents section duplicating its sibling page.

• Overview rewritten as two independent decisions: where users meet your agent (widget / your own UI via SDKs / phone / custom client) and who may start sessions (public agents vs authenticated sessions, with the comparison table moved here). States explicitly that every browser surface supports both access modes.
• authentication.mdx → authenticated-sessions.mdx (redirect added in docs.json): now the pure backend session-creation reference — token flow, request fields, response, token lifetime, force-end, errors — plus a client-agnostic table showing where the token goes per surface (Web SDK, React SDK, widget sessionTokenProvider, wire protocol).
• Sidebar reordered to setup order: overview → versions-publishing → public-agents → authenticated-sessions → widget → web-sdk → react-sdk → protocol.
• Mislink fixes: three pages cited the old Authentication page for "API key setup" (never covered there) — now point at api-reference/introduction or the console API-keys page; versions-publishing's "Automate via API" card pointed at the Deploy overview, now at the publish endpoint reference.
• Wording: "mint/minted/minting" → "create" across agent docs.
• CodeGroup cleanup: groups that tabbed different responsibilities (backend vs browser, draft-update vs publish, request vs response, distinct API operations) split into sequential blocks; tabs kept only for alternative implementations of the same action.

Verification

• mint broken-links: no broken links under agents/ (pre-existing temp/ template leftovers untouched)
• grep -riE '\bmint(s|ed|ing)?\b' over agent docs: clean (Mintlify brand excluded)
• Prettier: all touched files pass

🤖 Generated with Claude Code

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