None.get_saved is #35623. I believe it is related to #35379, where I requested your comment on what I found so far.
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1. Compiler warnings for shell input go to sys.__stderr, which only exists when IDLE is started from a console. This will include SyntaxWarnings when not turned into errors. pyshell 67+, warning_stream and idle_showwarning. I have no idea why. Compiler warnings for editor contents and runtime warnings go to shell. For now, all should go to Shell.
2. Warnings are formatted by run 42, idle_formatwarning. Someone must have decided that "<stdin>:1: DeprecationWarning: invalid escape sequence \e" is newbie unfriendly. When printed in an editor-derived window, the IDLE format will enable context menu 'goto file/line'. But 4 lines is a lot and the top line only serves to imitate the 'Traceback ...' line. I will think about this. Perhaps
DeprecationWarning: invalid escape sequence \e
File "<pyshell#1>", line 1
'\e'
3. Warnings (at least this one) for shell input are printed 3 times. I do not know why at present. ModifiedInterpreter.runsource calls code.InteractiveInterpreter(self, source, filename (pyshell 669). Perhaps the latter is buggy in somehow calling compile 3 times. I will look another time.