Fix broken badge link and add Fate logo to README

[rohans02]

Summary

Three small README fixes.

• Broken badge link. The Stability Nexus badge at the top pointed at https://stability.nexus/protocols, which returns 404. It now points at https://fate.stability.nexus/, the project landing page. This is a different site from the https://evm.fate.stability.nexus/ link in the body, which is the EVM app, so the two are complementary rather than duplicated.
• Fate logo added. The README showed only the organisation logo. The container was already display: flex; align-items: center; justify-content: center; gap: 16px holding a single image and an empty slot, so the mark now sits alongside rather than replacing it. Uses public/logo.svg from Replace Fate logo with new mark and fix broken icons #114.
• Removed <!-- Correct deployed url to be added -->. Obsolete once the badge points at the deployed URL, which is what the comment was asking for.

Swept every URL in the README while here. The other 22 resolve. news.stability.nexus returns 403 to a plain request but 200 with browser headers, so it is bot protection rather than a broken link.

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Summary by CodeRabbit

• Documentation
  • Updated README branding with the Fate Protocol logo.
  • Updated the organization badge link to the Fate Protocol website.

[coderabbitai]

No actionable comments were generated in the recent review. 🎉

ℹ️ Recent review info

⚙️ Run configuration

Configuration used: Path: .coderabbit.yaml

Review profile: ASSERTIVE

Plan: Pro Plus

Run ID: 50b40f8b-8aa5-473d-b789-a82482856e02

📥 Commits

Reviewing files that changed from the base of the PR and between 7709630 and 50f97fb.

📒 Files selected for processing (1)

• README.md

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Walkthrough

The README now displays the Fate Protocol logo, links the organization badge to https://evm.fate.stability.nexus/, and removes an obsolete deployment URL comment.

Changes

README branding

Layer / File(s)	Summary
Update README branding README.md	The README header includes the Fate Protocol logo. The organization badge links to the Fate Protocol site. The obsolete deployment URL comment is removed.

Estimated code review effort: 1 (Trivial) | ~2 minutes

Suggested labels: Documentation

Poem

A rabbit sees the logo shine,
And follows Fate’s updated line.
The badge points to its proper place,
The README shows its protocol face.
“Clean and clear!” the rabbit sings,
Then nibbles documentation strings.

🚥 Pre-merge checks | ✅ 4

✅ Passed checks (4 passed)

Check name	Status	Explanation
Description Check	✅ Passed	Check skipped - CodeRabbit’s high-level summary is enabled.
Title check	✅ Passed	The title clearly and concisely describes the README badge link fix and Fate logo addition.
Linked Issues check	✅ Passed	Check skipped because no linked issues were found for this pull request.
Out of Scope Changes check	✅ Passed	Check skipped because no linked issues were found for this pull request.

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• Create PR with unit tests

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