Terminal: ask what to connect to when Terminal is pressed with nothing open

The terminal surface with no session used to be an empty frame, with the tab row's "+" the only
thing on it that did anything. It now holds a prompt, in the order ssh asks: "connect to:" takes a
saved host's name, matched exactly, with the hosts that match so far listed under it for Tab or a
click, or user@host[:port] for a machine that is not saved. A password line follows only when one
is needed, worded as ssh words it. Escape steps back a line; recent connections are listed below.

It is drawn by Avalonia in the WebView's rectangle, which the occlusion rule allows because the two
are exclusive: the prompt shows only while there are no tabs, the WebView only for a tab with a
session.

Saved hosts connect through a new VaultViewModel.ConnectToHostAsync, which the drawer's own connect
now goes through too, so every refusal is still made once. Each attempt now carries whether it may
act on the drawer's remember-password tick, and the prompt's may not: otherwise a tick left on in
a closed drawer would save a password typed at a prompt that never offered to keep anything.

Covered by nine ShellFlowTests cases and four ConnectPromptTests; manual check 7.10b.

src/DodoSSH.Client.App/App.axaml

@@ -873,6 +873,29 @@
       <Setter Property="BorderBrush" Value="{StaticResource AccentSoft}" />
     </Style>
 
+    <!--
+      ◆ THE EMPTY TERMINAL'S PROMPT LINES, which are typed into the way a shell is: no fill, no border and no
+      padding in any state, so the text sits on the pane exactly where the label before it leaves off, and the
+      caret is the only sign the line takes input. A box drawn around it would turn a prompt back into a form.
+      See ConnectPrompt.axaml. After the base rules and .pathbox, for the reason this file keeps restating.
+    -->
+    <Style Selector="TextBox.prompt">
+      <Setter Property="FontFamily" Value="{StaticResource MonoFont}" />
+      <Setter Property="FontSize" Value="13" />
+      <Setter Property="Foreground" Value="{StaticResource Text}" />
+      <Setter Property="CaretBrush" Value="{StaticResource AccentText}" />
+      <Setter Property="MinHeight" Value="0" />
+      <Setter Property="Padding" Value="0" />
+      <Setter Property="VerticalContentAlignment" Value="Center" />
+    </Style>
+    <Style Selector="TextBox.prompt /template/ Border#PART_BorderElement,
+                     TextBox.prompt:pointerover /template/ Border#PART_BorderElement,
+                     TextBox.prompt:focus /template/ Border#PART_BorderElement">
+      <Setter Property="Background" Value="Transparent" />
+      <Setter Property="BorderBrush" Value="Transparent" />
+      <Setter Property="BorderThickness" Value="0" />
+    </Style>
+
     <!--
       Lists. The rows in this design are drawn by their own templates and marked as selected with an accent
       strip down the left edge, so the theme's rounded blue selection block has to go — it would sit behind