Hi Israel,
I'm Félix, the creator of LeoInteg. I'm glad to have people tryout LeoInteg! Thanks for giving it a try!! :)
I've successfully ran leointeg on many oses without any fuss, (windows, ubuntu, and even raspberry pi on a PI 3) using the simple commands shown here : (But I know sometimes it's not that simple or easy - so I'll try to help you out !)
First things first, to get you going, I gotta ask: what is this Leo 7.21 that you speak of? Are you from the future? 😅 the latest Leo is 6.7.4! (or 6.7.5 in development) Please take a screenshot of your Leo window at startup so we can see what you see here:

Next, take a screenshot of your LeoInteg Settings, which you can see if you use the "Welcome" command from LeoInteg in VSCode. (press F1 or Ctrl+shift+P to open the command palette, and start typing "Leo Welcome" to see the command and press enter) So that we can wee what you have setup, the screen looks like this (the important sections are "Leo-Editor Path" and "Python Command" ):
When you setup the options and press 'start server' on the LEO INTEGRATION panel on the left, you will see something like this in the Leo Output panel:
(Note: This command line is built with the options you put in the settings above)
Obviously you may get the error instead of a "success" but at least you will see what command LeoInteg tried to launch the server with. Please provide it in you reply so we can see, and diagnose a bit more.
Another good test that I would suggest, is to manually start the server to get better error messages : In a terminal, navigate to your Leo-Editor installation folder, then 'cd' into the /leo-editor/leo/core/ folder. Then, try to launch the leoserver.py script directly as such:
On my linux machine I can start it like this: python3.10 leoserver.py
On my windows machine i start it like this: py leoserver.py.
Try to see if you can start the server by launching it manually instead of automatically with LeoInteg, What does that do? Is it possible to start it successfully this way?
If it works you can then try connecting with leointeg with the 'Connect' button in the Leo Integration panel on the left. (no need to 'start' a server with leointeg if you started one manually.) And note what command you used in order to setup the settings in Leo's welcome screen properly. (perhaps you need to specify the python command as "py", "python", "python3" or "python3.11" or "python3.10" depending on what your setup is on your machine. Perhaps your "Leo-Editor" path was wrong. Or perhaps the websockets were installed on another python installation on your machine, different than the one that is used by leointeg when it tries to start the server itself. (in case you have many python installed on your machine, that is...)
(another possibility is websockets not installed properly)
When installing websockets with 'pip install websockets', make sure you're installing it to the right python installation that you intend to run the server with. (in case you have many python installations on your machine in various folders, like python2, python3. etc. or, with annaconda wich can let people use many different python installations on their machines.)
I've got to go now but i'll try later on my windows machine which also has python 3.11 like you have. In the meantime please try some of the stuff I suggested and (much importantly) take screenshots because often times it helps to spot something that you didn't think of mentionning!
Thanks again for trying out LeoInteg!!
Please provide feedback and screenshots so that we can help you out in figuring why it didn't work on you machine! :)
Félix