Make biomodel browsing public, gate LLM features behind login

[androemeda]

Summary

• /search, /chat, and /analyze no longer require login to load
• Login is now only enforced at the moment an LLM call would fire: sending a chat message, opening the "AI Analysis" tab on a biomodel's detail page, or clicking "Analyze Biomodel" — each shows a login-required popup instead
• Biomodel detail page's Overview tab is fully login-free (was previously making an authenticated call on load regardless of active tab)
• Sidebar shows "Log in to see your token usage" instead of a stuck "Loading..." when logged out
• No backend changes — vcelldb_router was already public and llms_router was already correctly auth-gated; this is purely frontend gating

[jcschaff]

looks good.