docs: refresh authored content to v0.16 (next; no version cut)

[0xrouss-miden]

Summary

Refreshes the docs-owned content from v0.15 to v0.16 so the authored Rust, TypeScript, React, MASM, and tool examples match the v0.16 API and toolchain line.

This PR prepares the current docs tree for the release. It does not create versioned_docs/version-0.16, update versions.json, or cut the stable snapshot; those remain part of a separate release PR.

static/llms.txt and static/skill.md intentionally carry the post-release 0.16 stable / 0.17 unstable labels. Merge must therefore be coordinated with the v0.16 snapshot cut to avoid publishing those labels early.

Out of scope

• The v0.16 migration guide, owned separately by docs(migration): add the v0.16 migration guide #357.
• Content imported at deploy time from protocol, Miden VM, node, rust-sdk, tutorials, note transport, and bridge portal.
• The final release manifest and generated v0.16 snapshot.

Changes

• Get Started — refresh setup, account, note, storage, and first-contract flows.
• Smart contracts — align account, note, transaction, standards, MASM, and Rust SDK guidance with v0.16.
• Web and React SDKs — update client setup, lifecycle, hooks, signers, transactions, and local-node testing.
• Tools and tutorial helpers — refresh Midenup, Playground, debugging, pitfalls, and testing guidance.
• Agent entrypoints — update llms.txt and skill.md for the repository split and v0.16 release context.
• Guardian ingestion — pin the tested v0.17.0-rc.1 documentation source.

Verification

• git diff --check origin/main...HEAD
• NODE_OPTIONS=--max-old-space-size=8192 npm run build
• Production build succeeds.
• No broken anchors originate from /next; remaining anchor warnings belong to historical snapshots or imported reference content.

Release gates

• v0.16.0 tags exist for node, rust-sdk, and web-sdk URLs referenced by these docs.
• Migration guide docs(migration): add the v0.16 migration guide #357 is merged by its owners.
• Final imported-content refs are selected and ready for the snapshot manifest.
• Merge is coordinated with the v0.16 snapshot cut.

Test plan

• CI deployment succeeds with all deploy-time imports.
• /next/ renders the v0.16 docs before the cut.
• After the separate snapshot PR, / serves v0.16 and /next/ advances to v0.17 unstable.