Hello there,
What you can do is use an external streaming app such as OBS Studio to record your live stream and then save it to your desktop. We actually always recommend our customer record externally as well ! Check out this article https://wpstream.net/should-i-record-locally-or-to-the-cloud/
You can then edit it and upload it to your website via WpStream or via one of the video shortcodes available. Note that if you simply upload the video to your website (not via WpStream), you will not be able to monetize it. Therefore, if you are not planning to monetize your videos, you do not need WpStream for your Recordings. Let me know if you have further questions!
Best,
Beatrice