[Python] How do I get UTF-8 to work flawlessly in modern PowerShell on Windows?

I have a C++ program which outputs raw UTF-8 and works flawlessly on Linux, but on Windows shells the output is not as nice. "®" turns into "┬«", "©" turns into "┬⌐", for example. There is also a Python part to the code, which seems to work better when printing to the shell, so I tried to test Python output a bit.

PS C:\Users\user> python -c 'print("\N{GREEK CAPITAL LETTER DELTA}")' > test_file_python.txt
Traceback (most recent call last):
File "<string>", line 1, in <module>
File "C:\Users\user\AppData\Local\Programs\Python\Python310\lib\encodings\cp1252.py", line 19, in encode
return codecs.charmap_encode(input,self.errors,encoding_table)[0]
UnicodeEncodeError: 'charmap' codec can't encode character '\u0394' in position 0: character maps to <undefined>
PS C:\Users\user> python -X utf8 -c 'print("\N{GREEK CAPITAL LETTER DELTA}")' > test_file_python.txt
PS C:\Users\user> cat test_file_python.txt
Δ
PS C:\Users\user> python -c 'print("\N{GREEK CAPITAL LETTER DELTA}")'
Δ
PS C:\Users\user> cat .\test_file_python_wsl.txt # Generated in WSL with the above commands
Δ
PS C:\Users\user> Format-Hex .\test_file_python.txt

Label: C:\Users\user\test_file_python.txt

Offset Bytes Ascii
00 01 02 03 04 05 06 07 08 09 0A 0B 0C 0D 0E 0F
------ ----------------------------------------------- -----
0000000000000000 E2 95 AC C3 B6 0D 0A �ö��

PS C:\Users\user> Format-Hex .\test_file_python_wsl.txt

Label: C:\Users\user\test_file_python_wsl.txt

Offset Bytes Ascii
00 01 02 03 04 05 06 07 08 09 0A 0B 0C 0D 0E 0F
------ ----------------------------------------------- -----
0000000000000000 CE 94 0A ��


I do not understand how PowerShell works with encoding, how can Python do this right when writing to the shell but not when redirecting, and why something that works perfectly in Linux Bash in WSL has this sort of issues in the newer cross-platform PowerShell Core which should "just work". These are multiple questions, but probably have a common answer.

EDIT: I forgot to add some important information, I am using PowerShell Core v7.3.6 with this encoding settings:

PS C:\Users\user> $OutputEncoding

Preamble :
BodyName : utf-8
EncodingName : Unicode (UTF-8)
HeaderName : utf-8
WebName : utf-8
WindowsCodePage : 1200
IsBrowserDisplay : True
IsBrowserSave : True
IsMailNewsDisplay : True
IsMailNewsSave : True
IsSingleByte : False
EncoderFallback : System.Text.EncoderReplacementFallback
DecoderFallback : System.Text.DecoderReplacementFallback
IsReadOnly : True
CodePage : 65001

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