docs: restructure README sponsor section and add pink fund button to docs

Fold the sponsor call-to-action into the Contributing section as a
natural bullet point instead of a standalone heavy section. Remove
the large badge buttons. Keep star history chart under Contributing.

Add a pink "Fund Development" button component to the docs site nav
bar (left of Star on GitHub), matching the landing page style.
Remove the plain-text nav link that replaced the heart icon.

apps/docs/.vitepress/theme/Layout.vue

@@ -1,6 +1,7 @@
 <script setup>
 import VPSwitchAppearance from "vitepress/dist/client/theme-default/components/VPSwitchAppearance.vue";
 import DefaultTheme from "vitepress/theme";
+import FundButton from "./FundButton.vue";
 import GitHubStars from "./GitHubStars.vue";
 
 const { Layout } = DefaultTheme;
@@ -11,6 +12,7 @@ const { Layout } = DefaultTheme;
     <template #nav-bar-content-after>
       <div class="nav-bar-right">
         <VPSwitchAppearance />
+        <FundButton />
         <GitHubStars />
       </div>
     </template>