ux: chat header + greeting + brain avatar + share button + terms + badge

Restores inline-JS styles.el (the obfuscated /assets/js/*.js path
broke the chat widget) and threads four UX fixes through it:

  - Chat header: drop the all-caps "NEURON / Live Demo" subtitle, keep
    just "Neuron" in bold white at 1rem.
  - Greeting: replace the canned "Hi. I am Neuron. You get 5 questions"
    with "Hey. What is on your mind?" in all three callsites (open,
    reset, turnstile-verified). The questions counter is already in
    the header, so we don't need to repeat it.
  - Avatar: switch chat avatar from neuron-icon.png to the brain mark
    (/assets/brand/neuron-brain.png). Thinking state now shows the
    pulsing brain plus three-dot animation instead of "thinking..."
    text.
  - Share button: from a muted t3 link to a navy pill with subtle
    background, uppercase letter-spacing, and active-press feedback.

main.el: drop the FOUNDING_SOLD = 47 floor and rewrite
fetch_founding_count_stripe to count succeeded PaymentIntents (the
live Stripe Elements path) AND legacy Checkout Sessions, excluding
refunded charges.

founding_badge.el: rewrite to the Option C "Tag" design picked from
/tmp/founding-badge-preview.html - tall card, navy top stroke, brain
mark prominent, "Neuron, LLC" footer.

terms.el: kill the "Neuron Inference - our own inference layer, live
now" claim. Inference launches Q3 2026 and the wording now says so.

src/terms.el

@@ -59,7 +59,7 @@ fn terms_body() -> String {
       <h2 style=\"font-family:var(--head);font-size:1.25rem;font-weight:600;color:var(--t1)\">Inference</h2>
     </div>
     <p style=\"font-family:var(--body);font-weight:300;font-size:0.9375rem;color:var(--t2);line-height:1.8;margin-bottom:1rem\">Neuron routes inference to whatever provider you configure - your own keys for OpenAI, Anthropic, Grok, any compatible endpoint. When you use a third-party provider, your prompts go through their infrastructure. Their terms apply. I don&#39;t control what they do with it.</p>
-    <p style=\"font-family:var(--body);font-weight:300;font-size:0.9375rem;color:var(--t2);line-height:1.8\">Neuron Inference - our own inference layer, live now - doesn&#39;t store your requests, doesn&#39;t train on them, doesn&#39;t share them. A separate data addendum covers the details.</p>
+    <p style=\"font-family:var(--body);font-weight:300;font-size:0.9375rem;color:var(--t2);line-height:1.8\">Neuron Inference - our own inference layer, launching Q3 2026 - will not store your requests, will not train on them, and will not share them. A separate data addendum will cover the details when it launches.</p>
   </div>
 
   <div style=\"margin-bottom:3rem\">