There is actually a workaround. Instead of using the "default" (persistent) live stream of your channel, use the "Live Control Room" to create a new stream. That will give you the possibility to uncheck the box next to "Publish to subscriptions feed and notify subscribers", which was grayed out when you used just the default persistent stream. But not sure whether it is automatically enabled after the video is published.
Another option, using the default persistent stream, is checking the box to set the created video as "unlisted" (you can keep the live stream public while the created video is set as unlisted after your live stream finishes), then uncheck the box "Publish in subscriber's feed and send notification", and after that set the video as "public". I can confirm that, in this case, the box remains unticked permanently.