Empty prompt effectively ends with newline

Closes gh-10138

IPython/terminal/prompts.py

@@ -62,11 +62,15 b' class RichPromptDisplayHook(DisplayHook):'
     """Subclass of base display hook using coloured prompt"""
     def write_output_prompt(self):
         sys.stdout.write(self.shell.separate_out)
-        self.prompt_end_newline = False
+        # If we're not displaying a prompt, it effectively ends with a newline,
+        # because the output will be left-aligned.
+        self.prompt_end_newline = True
+
         if self.do_full_cache:
             tokens = self.shell.prompts.out_prompt_tokens()
-            if tokens and tokens[-1][1].endswith('\n'):
-                self.prompt_end_newline = True
+            if tokens and not tokens[-1][1].endswith('\n'):
+                # Ask for a newline before multiline output
+                self.prompt_end_newline = False
             if self.shell.pt_cli:
                 self.shell.pt_cli.print_tokens(tokens)
             else: