What you are showing in that screenshot is Jupyter Notebook 7+. You now choose the document type you want to open in ‘New’. So if you choose ‘Notebook’, when that opens you should get the option to choose the type of kernel. Pick the ‘Python’ one there. ‘Python3’ is probably not involved on newer computers. That is an old alias for things when Python 2.7 was still fairly common. Now that isn’t supported and so in general you just need Python and it will indeed be Python 3. I suspect you are expecting ‘Python’ of some sort to be listed under ‘New’ because of the old interface and so you may want to read here about the recent changes and follow the link there to learn more.
One issue you may encounter though is that your kernel may not be using the 3.12.2 you installed. You didn’t tell us at all how you installed things and so it may work as you expect. It may not.
One option is to instead of handling Python and Jupyter installation yourself is to install the Anaconda Distribution on your machine and then use Python and Jupyter through the Anaconda Navigator. It may not come with Python 3.12 by default at this time as it tries to give tried and tested combinations of the Python/Jupyter ecosystem in the base install. If you go that route, you’ll want to read about how to further modify Anaconda to have the environments you want. Because that requires some extra learning to use the features to the fullest, some people find this a challenge.