まだまだ続きます。DirectCompositionを絡めた表示に修正してみます。
自分でも未消化なので、まだメモ止まりです。。。
用語が決まっていないと説明しにくいです。

Initialize()

下記3種で比較します。

USE_CONTEXT:
(前回のDXGIスワップチェーン描画)
DXGIスワップチェーンを作成し、そのサーファスをデバイスコンテキストに割り当てる

USE_DCOMP1:
DirectCompositionの、HWND = Target -> Visual -> Content の階層構造において、
新規に作成したサーファスをContentとして割り当てる

USE_DCOMP2:
DXGIスワップチェーンを作成し、そのサーファスをデバイスコンテキストに割り当てるとともに、
DirectCompositionの、HWND = Target -> Visual -> Content の階層構造において、
DXGIスワップチェーンをContentとしても割り当てる

# include <dcomp.h>
# pragma comment(lib, "dcomp.lib")

IDCompositionDesktopDevice *pDComp_Device;
IDCompositionTarget        *pDComp_Target;
IDCompositionVisual2       *pDComp_RootVisual;
IDCompositionSurface       *pDComp_Surface;

//#define  USE_CONTEXT
//#define  USE_DCOMP1
# define    USE_DCOMP2

# ifdef USE_CONTEXT
  pD2D_Device->CreateDeviceContext(D2D1_DEVICE_CONTEXT_OPTIONS_NONE, reinterpret_cast<ID2D1DeviceContext **>(&pDC));

  CreateDXGIFactory2(0, IID_PPV_ARGS(&pDXGI_Factory));
  DXGI_SWAP_CHAIN_DESC1 swapChainDesc={};
  swapChainDesc.Format=DXGI_FORMAT_B8G8R8A8_UNORM;
  swapChainDesc.BufferUsage=DXGI_USAGE_RENDER_TARGET_OUTPUT;
  swapChainDesc.SwapEffect=DXGI_SWAP_EFFECT_FLIP_SEQUENTIAL;
  swapChainDesc.BufferCount=2;
  swapChainDesc.SampleDesc.Count=1;
  pDXGI_Factory->CreateSwapChainForHwnd(pDXGI_Device, hDlgImg, &swapChainDesc, NULL, NULL, &pDXGI_SwapChain);
  pDXGI_SwapChain->GetBuffer(0, IID_PPV_ARGS(&pDXGI_Surface));

  D2D1_BITMAP_PROPERTIES1 bitmapPropsDXGI=D2D1::BitmapProperties1(D2D1_BITMAP_OPTIONS_NONE, D2D_PixelFormat);
  bitmapPropsDXGI.bitmapOptions|=(D2D1_BITMAP_OPTIONS_TARGET|D2D1_BITMAP_OPTIONS_CANNOT_DRAW);
  pDC->CreateBitmapFromDxgiSurface(pDXGI_Surface, &bitmapPropsDXGI, &pD2D_BitmapDXGI);
  pDC->SetTarget(pD2D_BitmapDXGI);
# endif

# ifdef USE_DCOMP1
  DCompositionCreateDevice2(pD2D_Device, IID_PPV_ARGS(&pDComp_Device));
  pDComp_Device->QueryInterface(IID_PPV_ARGS(&pDComp_DeviceEffect));
  pDComp_Device->CreateTargetForHwnd(hDlgImg, TRUE, &pDComp_Target);
  pDComp_Device->CreateVisual(&pDComp_RootVisual);
  pDComp_Device->CreateSurface(FrameWidth, FrameHeight, DXGI_FORMAT_B8G8R8A8_UNORM, DXGI_ALPHA_MODE_IGNORE, &pDComp_Surface);
  pDComp_Target->SetRoot(pDComp_RootVisual);
  pDComp_RootVisual->SetContent(pDComp_Surface);
# endif
  
# ifdef USE_DCOMP2

  pD2D_Device->CreateDeviceContext(D2D1_DEVICE_CONTEXT_OPTIONS_NONE, reinterpret_cast<ID2D1DeviceContext **>(&pDC));

  CreateDXGIFactory2(0, IID_PPV_ARGS(&pDXGI_Factory));
  DXGI_SWAP_CHAIN_DESC1 swapChainDesc={};
  swapChainDesc.Format=DXGI_FORMAT_B8G8R8A8_UNORM;
  swapChainDesc.BufferUsage=DXGI_USAGE_RENDER_TARGET_OUTPUT;
  swapChainDesc.SwapEffect=DXGI_SWAP_EFFECT_FLIP_SEQUENTIAL;
  swapChainDesc.BufferCount=2;
  swapChainDesc.SampleDesc.Count=1;
  swapChainDesc.Width=FrameWidth;
  swapChainDesc.Height=FrameHeight;
  pDXGI_Factory->CreateSwapChainForComposition(pDXGI_Device, &swapChainDesc, NULL, &pDXGI_SwapChain);
  pDXGI_SwapChain->GetBuffer(0, IID_PPV_ARGS(&pDXGI_Surface));

  D2D1_BITMAP_PROPERTIES1 bitmapPropsDXGI=D2D1::BitmapProperties1(D2D1_BITMAP_OPTIONS_NONE, D2D_PixelFormat);
  bitmapPropsDXGI.bitmapOptions|=(D2D1_BITMAP_OPTIONS_TARGET|D2D1_BITMAP_OPTIONS_CANNOT_DRAW);
  pDC->CreateBitmapFromDxgiSurface(pDXGI_Surface, &bitmapPropsDXGI, &pD2D_BitmapDXGI);
  pDC->SetTarget(pD2D_BitmapDXGI);

  DCompositionCreateDevice2(pD2D_Device, IID_PPV_ARGS(&pDComp_Device));
  pDComp_Device->QueryInterface(IID_PPV_ARGS(&pDComp_DeviceEffect));
  pDComp_Device->CreateTargetForHwnd(hDlgImg, TRUE, &pDComp_Target);
  pDComp_Device->CreateVisual(&pDComp_RootVisual);
  pDComp_Device->CreateSurface(FrameWidth, FrameHeight, DXGI_FORMAT_B8G8R8A8_UNORM, DXGI_ALPHA_MODE_IGNORE, &pDComp_Surface);
  pDComp_Target->SetRoot(pDComp_RootVisual);
  pDComp_RootVisual->SetContent(pDXGI_SwapChain);
  pDComp_Device->Commit();
# endif

描画処理

USE_CONTEXT, USE_DCOMP2:
DXGIスワップチェーンから派生したデバイスコンテキストに対して描画処理し、Presentする

USE_DCOMP1:
DirectCompositionのContentから一時的に作成したデバイスコンテキストに対して描画処理し、Commitする

# if defined USE_CONTEXT
      pDC->BeginDraw();
      pDC->SetTransform(D2D1::Matrix3x2F::Identity());
      pDC->Clear(D2D1::ColorF(D2D1::ColorF::Black));
      if(pD2D_Bitmap!=NULL){
        pDC->DrawBitmap(pD2D_Bitmap, D2D1::RectF(0.f, 0.f, (float)ImageWidth1, (float)ImageHeight1),
                        1.f, D2D1_BITMAP_INTERPOLATION_MODE_LINEAR);
      }
      wchar_t wbuf[256]; MultiByteToWideChar(CP_ACP, 0, "test", -1, wbuf, 256);
      pDC->DrawText(wbuf, wcslen(wbuf), pFont, D2D1::RectF(0, 0, 100, 20), pBrush);
      pDC->EndDraw();

# elif defined USE_DCOMP1
      POINT offset={};
      ID2D1DeviceContext *pDCtemp;
      pDComp_Surface->BeginDraw(NULL, IID_PPV_ARGS(&pDCtemp), &offset);
      pDCtemp->SetTransform(D2D1::Matrix3x2F::Translation((float)offset.x, (float)offset.y));
      pDCtemp->Clear(D2D1::ColorF(D2D1::ColorF::Black));
      if(pD2D_Bitmap!=NULL){
        pDCtemp->DrawBitmap(pD2D_Bitmap, D2D1::RectF(0.f, 0.f, (float)ImageWidth1, (float)ImageHeight1),
                            1.f, D2D1_BITMAP_INTERPOLATION_MODE_LINEAR);
      }
      wchar_t wbuf[256]; MultiByteToWideChar(CP_ACP, 0, "test", -1, wbuf, 256);
      pDCtemp->DrawText(wbuf, wcslen(wbuf), pFont, D2D1::RectF(0, 0, 100, 20), pBrush);
      pDComp_Surface->EndDraw();
      pDCtemp->Release();

# elif defined USE_DCOMP2
      pDC->BeginDraw();
      pDC->SetTransform(D2D1::Matrix3x2F::Identity());
      pDC->Clear(D2D1::ColorF(D2D1::ColorF::Black));
      if(pD2D_Bitmap!=NULL){
        pDC->DrawBitmap(pD2D_Bitmap, D2D1::RectF(0.f, 0.f, (float)ImageWidth1, (float)ImageHeight1),
                        1.f, D2D1_BITMAP_INTERPOLATION_MODE_LINEAR);
      }
      wchar_t wbuf[256]; MultiByteToWideChar(CP_ACP, 0, "test", -1, wbuf, 256);
      pDC->DrawText(wbuf, wcslen(wbuf), pFont, D2D1::RectF(0, 0, 100, 20), pBrush);
      pDC->EndDraw();
# endif
      
# ifdef defined USE_CONTEXT || defined USE_DCOMP2
      pDXGI_SwapChain->Present(1, 0);
# elif defined USE_DCOMP1
      pDComp_Device->Commit();
# endif
      ValidateRect(hDlgImg, NULL);
    }