Add New Chat Button

Nucleic-Session: BB7AA593-185A-4A8F-A3DA-598EE63874E2
Co-authored-by: Nucleic <[email protected]>

NucleicRemote/NucleicRemote/Views/SessionsView.swift

@@ -89,10 +89,50 @@ struct SessionsView: View {
                     }
                 }
             }
+            // A floating "new chat" affordance in the lower-right, mirroring the Mac's per-project
+            // "New chat" button. Picks a project + prompt in a sheet, then kicks off the chat.
+            .overlay(alignment: .bottomTrailing) {
+                if canStartChat { newChatButton }
+            }
+            .sheet(isPresented: $showNewChat) {
+                NavigationStack {
+                    ScrollView {
+                        StartChatComposer(onStart: { showNewChat = false })
+                            .padding()
+                    }
+                    .navigationTitle("New chat")
+                    .navigationBarTitleDisplayMode(.inline)
+                    .toolbar {
+                        ToolbarItem(placement: .topBarLeading) {
+                            Button("Cancel") { showNewChat = false }
+                        }
+                    }
+                }
+                .presentationDetents([.medium, .large])
+            }
             .safeAreaInset(edge: .bottom) { ConnectionChip().padding(.bottom, 8) }
         }
     }
 
+    /// The circular plus button, styled to match the transcript's jump-to-bottom FAB: an accent
+    /// disc with a soft shadow, floated clear of the connection chip.
+    private var newChatButton: some View {
+        Button {
+            showNewChat = true
+        } label: {
+            Image(systemName: "plus")
+                .font(.system(size: 22, weight: .semibold))
+                .foregroundStyle(.white)
+                .frame(width: 56, height: 56)
+                .background(Palette.accent, in: .circle)
+                .shadow(color: .black.opacity(0.25), radius: 6, y: 2)
+        }
+        .buttonStyle(.plain)
+        .padding(.trailing, 20)
+        .padding(.bottom, 20)
+        .accessibilityLabel("New chat")
+    }
+
     /// Push the session a notification tap asked for, then clear the request.
     private func consumeRoute() {
         guard let route = store.pendingRoute else { return }