[Conpty] Pass through request for mouse mode to the Terminal (#9970)

<!-- Enter a brief description/summary of your PR here. What does it fix/what does it change/how was it tested (even manually, if necessary)? -->
## Summary of the Pull Request
When the client application sets the console input mode with the `ENABLE_MOUSE_INPUT` flag, we send along the appropriate VT sequences to the connected terminal (if there is one).

<!-- Other than the issue solved, is this relevant to any other issues/existing PRs? --> 
## References
#376 
#6859 

<!-- Please review the items on the PR checklist before submitting-->
## PR Checklist
* [ ] Closes #xxx
* [x] CLA signed. If not, go over [here](https://cla.opensource.microsoft.com/microsoft/Terminal) and sign the CLA
* [ ] Tests added/passed
* [ ] Documentation updated. If checked, please file a pull request on [our docs repo](https://github.com/MicrosoftDocs/terminal) and link it here: #xxx
* [ ] Schema updated.
* [x] I work here

<!-- Describe how you validated the behavior. Add automated tests wherever possible, but list manual validation steps taken as well -->
## Validation Steps Performed
Far manager works

src/host/VtIo.cpp

@@ -213,6 +213,7 @@ bool VtIo::IsUsingVt() const
         {
             g.pRender->AddRenderEngine(_pVtRenderEngine.get());
             g.getConsoleInformation().GetActiveOutputBuffer().SetTerminalConnection(_pVtRenderEngine.get());
+            g.getConsoleInformation().GetActiveInputBuffer()->SetTerminalConnection(_pVtRenderEngine.get());
         }
         CATCH_RETURN();
     }

src/host/getset.cpp

@@ -334,6 +334,8 @@ void ApiRoutines::GetNumberOfConsoleMouseButtonsImpl(ULONG& buttons) noexcept
         LockConsole();
         auto Unlock = wil::scope_exit([&] { UnlockConsole(); });
 
+        const auto oldQuickEditMode{ WI_IsFlagSet(gci.Flags, CONSOLE_QUICK_EDIT_MODE) };
+
         if (WI_IsAnyFlagSet(mode, PRIVATE_MODES))
         {
             WI_SetFlag(gci.Flags, CONSOLE_USE_PRIVATE_FLAGS);
@@ -357,6 +359,19 @@ void ApiRoutines::GetNumberOfConsoleMouseButtonsImpl(ULONG& buttons) noexcept
             WI_ClearFlag(gci.Flags, CONSOLE_USE_PRIVATE_FLAGS);
         }
 
+        const auto newQuickEditMode{ WI_IsFlagSet(gci.Flags, CONSOLE_QUICK_EDIT_MODE) };
+
+        // Mouse input should be received when mouse mode is on and quick edit mode is off
+        // (for more information regarding the quirks of mouse mode and why/how it relates
+        //  to quick edit mode, see GH#9970)
+        const auto oldMouseMode{ !oldQuickEditMode && WI_IsFlagSet(context.InputMode, ENABLE_MOUSE_INPUT) };
+        const auto newMouseMode{ !newQuickEditMode && WI_IsFlagSet(mode, ENABLE_MOUSE_INPUT) };
+
+        if (oldMouseMode != newMouseMode)
+        {
+            gci.GetActiveInputBuffer()->PassThroughWin32MouseRequest(newMouseMode);
+        }
+
         context.InputMode = mode;
         WI_ClearAllFlags(context.InputMode, PRIVATE_MODES);
 

src/host/inputBuffer.cpp

@@ -15,6 +15,7 @@
 
 using Microsoft::Console::Interactivity::ServiceLocator;
 using Microsoft::Console::VirtualTerminal::TerminalInput;
+using namespace Microsoft::Console;
 
 // Routine Description:
 // - This method creates an input buffer.
@@ -25,6 +26,7 @@ using Microsoft::Console::VirtualTerminal::TerminalInput;
 InputBuffer::InputBuffer() :
     InputMode{ INPUT_BUFFER_DEFAULT_INPUT_MODE },
     WaitQueue{},
+    _pTtyConnection(nullptr),
     _termInput(std::bind(&InputBuffer::_HandleTerminalInputCallback, this, std::placeholders::_1))
 {
     // The _termInput's constructor takes a reference to this object's _HandleTerminalInputCallback.
@@ -218,6 +220,26 @@ void InputBuffer::FlushAllButKeys()
     _storage.erase(newEnd, _storage.end());
 }
 
+void InputBuffer::SetTerminalConnection(_In_ ITerminalOutputConnection* const pTtyConnection)
+{
+    this->_pTtyConnection = pTtyConnection;
+}
+
+void InputBuffer::PassThroughWin32MouseRequest(bool enable)
+{
+    if (_pTtyConnection)
+    {
+        if (enable)
+        {
+            LOG_IF_FAILED(_pTtyConnection->WriteTerminalW(L"\x1b[?1003;1006h"));
+        }
+        else
+        {
+            LOG_IF_FAILED(_pTtyConnection->WriteTerminalW(L"\x1b[?1003;1006l"));
+        }
+    }
+}
+
 // Routine Description:
 // - This routine reads from the input buffer.
 // - It can convert returned data to through the currently set Input CP, it can optionally return a wait condition

src/host/inputBuffer.hpp

@@ -26,6 +26,8 @@ Revision History:
 #include "../server/ObjectHeader.h"
 #include "../terminal/input/terminalInput.hpp"
 
+#include "../inc/ITerminalOutputConnection.hpp"
+
 #include <deque>
 
 class InputBuffer final : public ConsoleObjectHeader
@@ -75,12 +77,15 @@ public:
 
     bool IsInVirtualTerminalInputMode() const;
     Microsoft::Console::VirtualTerminal::TerminalInput& GetTerminalInput();
+    void SetTerminalConnection(_In_ Microsoft::Console::ITerminalOutputConnection* const pTtyConnection);
+    void PassThroughWin32MouseRequest(bool enable);
 
 private:
     std::deque<std::unique_ptr<IInputEvent>> _storage;
     std::unique_ptr<IInputEvent> _readPartialByteSequence;
     std::unique_ptr<IInputEvent> _writePartialByteSequence;
     Microsoft::Console::VirtualTerminal::TerminalInput _termInput;
+    Microsoft::Console::ITerminalOutputConnection* _pTtyConnection;
 
     // This flag is used in _HandleTerminalInputCallback
     // If the InputBuffer leads to a _HandleTerminalInputCallback call,