Add file badges, menu icons, LSP diagnostics, robust compaction

- Files in chat: preview with type/size badges and file name; attachment chips
- Menu and settings tabs with icons
- Heatmap: distinct colour for empty hours, hourly labels
- Context chip shows used/total tokens (e.g. 221k/240k) plus percent
- LSP client: diagnostics appended to edit/write results and a diagnostics tool
  (typescript-language-server, pyright, rust-analyzer, gopls, clangd; sandboxed)
- Compaction summarizes a plain transcript and retries once on empty output
- files/stat endpoint

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

server/src/app.rs

@@ -69,6 +69,8 @@ pub struct App {
     pub tool_install: crate::reverse::ToolInstall,
     /// Background shells of all sessions.
     pub shells: crate::shells::Shells,
+    /// Language servers (diagnostics after edits).
+    pub lsp: crate::lsp::Lsp,
 }
 
 /// What a user may do with a session.
@@ -105,6 +107,7 @@ impl App {
             login_failures: Mutex::default(),
             tool_install: Mutex::default(),
             shells: Mutex::default(),
+            lsp: Default::default(),
         });
         crate::auth::bootstrap(&app)?;
         app.clone().start_mcp();