This was my first thought when seeing the video.
I let my young pullets out for the first time to free range. It had rained for a few days before and they were in and out of the woods.
The next day 2 hung their heads to the ground as if their necks were snapped and 2 behaved like your rooster. Except for their heads and neck, they were fine.
I quickly dosed with epsom salts and the 2 with mild symptoms recovered within hours. The 2 dragging their heads did not survive.
Botulism can be found in wet feed and also several places after a lot of rain. In the woods under leaves for instance, old fruit and vegetables left in a pen, etc.
My older birds seem to be more immune than younger penned birds are. They either know not to scratch around in certain areas or their immune system is stronger.
They can also recover on their own if it is just a mild case. Within 36 hours, you will know if they will live or die. Its a fast passing poison.
There are also a wide variety of symptoms. This is just how mine presented theirs.
I never had lingering symptoms but I wonder if there can be long lasting neurological effects from the toxin. Something to study on maybe?
This is my experience.