Ignore closeOnExit when a connection moves to Failed w/o being Connected

ConptyConnection has two different failure modes:

1. We failed to initialize the pseudoconsole or create the process
2. The process exited with an error code.

Until this commit, they were treated the same way: closeOnExit=always
would force the pane/tab to be destroyed. This was very bad in case 1,
where we would display a (possibly useful) error message and then
immediately close the window.

This was made even worse by the change in #10045. We removed
startingDirectory validation and promoted it to an error message (so
that we could eventually let the connection handle startingDirectory in
its own way.) This of course revealed that a number of users had set
invalid starting directories… and those users included some who set
closeOnExit to always. Boom: instant "terminal opens and crashes"¹

¹ It only looks like a crash; it's actually _technically_ functioning
properly.

Closes #10225.

src/cascadia/TerminalApp/Pane.cpp

@@ -329,13 +329,22 @@ void Pane::_ControlConnectionStateChangedHandler(const winrt::Windows::Foundatio
     }
 
     const auto newConnectionState = _control.ConnectionState();
+    const auto previousConnectionState = std::exchange(_connectionState, newConnectionState);
 
     if (newConnectionState < ConnectionState::Closed)
     {
         // Pane doesn't care if the connection isn't entering a terminal state.
         return;
     }
 
+    if (previousConnectionState < ConnectionState::Connected && newConnectionState >= ConnectionState::Failed)
+    {
+        // A failure to complete the connection (before it has _connected_) is not covered by "closeOnExit".
+        // This is to prevent a misconfiguration (closeOnExit: always, startingDirectory: garbage) resulting
+        // in Terminal flashing open and immediately closed.
+        return;
+    }
+
     const auto settings{ winrt::TerminalApp::implementation::AppLogic::CurrentAppSettings() };
     auto paneProfile = settings.FindProfile(_profile.value());
     if (paneProfile)
@@ -709,6 +718,7 @@ void Pane::_CloseChild(const bool closeFirst)
 
         // take the control, profile and id of the pane that _wasn't_ closed.
         _control = remainingChild->_control;
+        _connectionState = remainingChild->_connectionState;
         _profile = remainingChild->_profile;
         _id = remainingChild->Id();
 
@@ -1476,6 +1486,7 @@ std::pair<std::shared_ptr<Pane>, std::shared_ptr<Pane>> Pane::_Split(SplitState
     //   Move our control, guid into the first one.
     //   Move the new guid, control into the second.
     _firstChild = std::make_shared<Pane>(_profile.value(), _control);
+    _firstChild->_connectionState = std::exchange(_connectionState, ConnectionState::NotConnected);
     _profile = std::nullopt;
     _control = { nullptr };
     _secondChild = std::make_shared<Pane>(profile, control);

src/cascadia/TerminalApp/Pane.h

@@ -95,6 +95,7 @@ class Pane : public std::enable_shared_from_this<Pane>
     winrt::Windows::UI::Xaml::Controls::Grid _root{};
     winrt::Windows::UI::Xaml::Controls::Border _border{};
     winrt::Microsoft::Terminal::Control::TermControl _control{ nullptr };
+    winrt::Microsoft::Terminal::TerminalConnection::ConnectionState _connectionState{ winrt::Microsoft::Terminal::TerminalConnection::ConnectionState::NotConnected };
     static winrt::Windows::UI::Xaml::Media::SolidColorBrush s_focusedBorderBrush;
     static winrt::Windows::UI::Xaml::Media::SolidColorBrush s_unfocusedBorderBrush;
 

src/cascadia/TerminalConnection/ConptyConnection.cpp

@@ -251,6 +251,8 @@ namespace winrt::Microsoft::Terminal::TerminalConnection::implementation
     void ConptyConnection::Start()
     try
     {
+        _transitionToState(ConnectionState::Connecting);
+
         if (!_inPipe)
         {
             const COORD dimensions{ gsl::narrow_cast<SHORT>(_initialCols), gsl::narrow_cast<SHORT>(_initialRows) };