Add TypeScript migration, image resizing, media upload UX, and multimedia support

- Migrate static JS to TypeScript (static-ts/ → compiled to internal/api/static/)
- Add image resizing on upload: JPEG/PNG/WebP scaled to max 1920px at quality 80
- Extract shared upload logic into upload.go (saveUpload, saveResizedImage, saveResizedWebP)
- Add POST /media endpoint for drag-drop/paste media uploads with markdown ref return
- Add background music player with video/audio coordination (autoplay.ts)
- Add global nav, public feed, hashtags, visibility, Markdown rendering for entries
- Add Dockerfile stage for TypeScript compilation (static-ts-builder)
- Add goldmark, disintegration/imaging, golang.org/x/image dependencies

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

backend/internal/api/templates/public.html

@@ -12,14 +12,22 @@
 {{range .Entries}}
 <article class="pub-card">
   {{if .Images}}
-  <a href="/uploads/{{(index .Images 0).Filename}}" target="_blank">
-    <img class="pub-cover" src="/uploads/{{(index .Images 0).Filename}}" alt="">
+  {{with (index .Images 0)}}
+  {{if isVideo .MimeType}}
+  <video src="/uploads/{{.Filename}}" controls class="media-embed"></video>
+  {{else if isAudio .MimeType}}
+  <audio src="/uploads/{{.Filename}}" controls class="media-audio"></audio>
+  {{else}}
+  <a href="/uploads/{{.Filename}}" target="_blank">
+    <img class="pub-cover" src="/uploads/{{.Filename}}" alt="">
   </a>
   {{end}}
+  {{end}}
+  {{end}}
   <div class="pub-body">
     <small class="pub-meta">{{.EntryDate}} · {{.EntryTime}}</small>
     {{if .Title}}<strong class="pub-title">{{.Title}}</strong>{{end}}
-    {{if .Description}}<p class="pub-desc">{{.Description}}</p>{{end}}
+    {{if .Description}}<div class="pub-desc">{{markdown .Description}}</div>{{end}}
     {{if .Hashtags}}<div class="pub-tags">{{range .Hashtags}}<span class="tag">#{{.}}</span> {{end}}</div>{{end}}
   </div>
 </article>