Add scratchpad_delete MCP tool

Mirrors the existing scratchpad_* tools end-to-end: catalog schema,
dispatch, ToolHost.ScratchpadDelete, and a host method that delegates to
scratchpad.Store.Delete and fires scratchpadsChanged() on success so the
sidebar refreshes. Missing-pad errors surface rather than being masked.

Resolves the [MCP SCRATCHPAD DELETE] TODO item.

internal/app/scratchpad_delete_test.go

@@ -1,10 +1,12 @@
 package app
 
 import (
+	"errors"
 	"io"
 	"os"
 	"testing"
 
+	"github.com/hjbdev/patterm/internal/preset"
 	"github.com/hjbdev/patterm/internal/scratchpad"
 )
 
@@ -95,3 +97,41 @@ func TestDeletingLastFocusedScratchpadFocusesRunningChild(t *testing.T) {
 		t.Fatalf("focusedID = %q, want pid", st.focusedID)
 	}
 }
+
+type scratchpadChangeRecorder struct {
+	count int
+}
+
+func (r *scratchpadChangeRecorder) scratchpadsChanged() {
+	r.count++
+}
+
+func TestToolHostScratchpadDeleteRemovesPadAndRefreshes(t *testing.T) {
+	t.Setenv("XDG_DATA_HOME", t.TempDir())
+	pads, err := scratchpad.Open("scratchpad-delete-host-test")
+	if err != nil {
+		t.Fatalf("scratchpad.Open: %v", err)
+	}
+	if _, err := pads.Write("doomed.md", "content", ""); err != nil {
+		t.Fatalf("write doomed.md: %v", err)
+	}
+	recorder := &scratchpadChangeRecorder{}
+	host := newToolHost(nil, pads, nil, preset.Set{}, nil, 120, 40)
+	host.scratch = recorder
+
+	if err := host.ScratchpadDelete("doomed.md"); err != nil {
+		t.Fatalf("ScratchpadDelete: %v", err)
+	}
+	if recorder.count != 1 {
+		t.Fatalf("scratchpadsChanged calls = %d, want 1", recorder.count)
+	}
+	if _, _, err := pads.Read("doomed.md"); !errors.Is(err, os.ErrNotExist) {
+		t.Fatalf("read deleted pad error = %v, want os.ErrNotExist", err)
+	}
+	if err := host.ScratchpadDelete("doomed.md"); !errors.Is(err, os.ErrNotExist) {
+		t.Fatalf("delete missing error = %v, want os.ErrNotExist", err)
+	}
+	if recorder.count != 1 {
+		t.Fatalf("scratchpadsChanged calls after failed delete = %d, want 1", recorder.count)
+	}
+}