feat: another wave of features (#61)

## Explanation

This PR bundles several user-facing improvements and feature additions for the v0.3.0 release, including quality-of-life improvements to the UI, new slash commands, better state persistence, and auto-update checking.

## Included Changes

- **Resizable chat input** with drag handle (#58 partial)
- **Arrow key navigation fix** - cursor keys now navigate text when user has typed input (#58)
- **Scroll position persistence** per conversation tab
- **/skill command** for invoking Claude Code skills (#57)
- **Stats persistence fix** - stats now persist across session changes, only reset on disconnect (#59)
- **Auto-update checker** on startup (#17)
- **Resizable character panel** with full-height sprites (#10)
- **Font size and zoom settings** with keyboard shortcuts (Ctrl++/Ctrl+-/Ctrl+0) (#19)

## Closes

Closes #10, #17, #19, #57, #58, #59

## Attestations

- [x] I have read and agree to the Code of Conduct
- [x] I have read and agree to the Community Guidelines
- [x] My contribution complies with the Contributor Covenant
- [x] I have run the linter and resolved any errors
- [x] My pull request uses an appropriate title, matching the conventional commit standards
- [x] My scope of feat/fix/chore/etc. correctly matches the nature of changes in my pull request
- [x] All new and existing tests pass locally with my changes
- [x] Code coverage remains at or above the configured threshold

## Documentation

N/A - Internal app features

## Versioning

Minor - My pull request introduces new non-breaking features.

---
✨ This PR was created with help from Hikari~ 🌸

Co-authored-by: Hikari <hikari@nhcarrigan.com>
Reviewed-on: #61
Co-authored-by: Naomi Carrigan <commits@nhcarrigan.com>
Co-committed-by: Naomi Carrigan <commits@nhcarrigan.com>

src/lib/components/AnimeGirl.svelte

@@ -57,30 +57,34 @@
   }
 </script>
 
-<div class="anime-girl-container flex flex-col items-center justify-end h-full p-4">
-  <div class="character-frame relative {getBackgroundGlow()} w-full max-w-md">
-    <div class="sprite-container {getAnimationClass()}">
+<div
+  class="anime-girl-container flex flex-col items-center justify-between h-full p-4 overflow-hidden"
+>
+  <div
+    class="character-frame relative {getBackgroundGlow()} flex-1 flex items-center justify-center min-h-0"
+  >
+    <div class="sprite-container {getAnimationClass()} h-full flex items-center justify-center">
       <img
         src="/sprites/{info.spriteFile}"
         alt="Hikari - {info.label}"
-        class="character-sprite w-full h-auto object-contain"
+        class="character-sprite h-full w-auto max-w-full object-contain"
         onerror={(e) => {
           const target = e.currentTarget as HTMLImageElement;
           target.src = "/sprites/placeholder.svg";
         }}
       />
     </div>
+  </div>
 
-    <div class="state-indicator absolute -bottom-2 left-1/2 transform -translate-x-1/2">
-      <div
-        class="px-3 py-1 rounded-full text-xs font-medium bg-[var(--bg-secondary)] border border-[var(--border-color)] text-[var(--accent-primary)]"
-      >
-        {info.label}
-      </div>
+  <div class="state-indicator mt-2">
+    <div
+      class="px-3 py-1 rounded-full text-xs font-medium bg-[var(--bg-secondary)] border border-[var(--border-color)] text-[var(--accent-primary)]"
+    >
+      {info.label}
     </div>
   </div>
 
-  <div class="speech-bubble mt-4 max-w-xs">
+  <div class="speech-bubble mt-2 max-w-xs flex-shrink-0">
     <div
       class="relative bg-[var(--bg-secondary)] rounded-lg px-4 py-2 border border-[var(--border-color)]"
     >