You’d process each of them less than half as well as if you’d watched it on its own?

You cannot. If you tried you’d just be watching one and then the other, with your brain interpolating between takes.

Try it, for science. Then try and recall b o th shows separately.

Take lots of stimulant beforehand, and maybe slow down each shows’ playback by 10-20%, I see no problem with this pass-time (I would get a headache after 3 minutes or so of trying, especially so if they were completely different shows, or are both from a show I have not seen yet).

You’re not gonna remember them both particularly well.

Source: I split my laptop screen into pieces with video and games, and both suffer for it

When "multitasking", the brain rapidly switches between processing the different tasks.

Most areas of our brain can only do 1 task at a time. If you try and do more, it flips rapidly between them. Basically, you would “watch” vaguely 30-50% of each show, with your brain trying to fill in the gaps.

Interestingly, you can do 2 tasks that don’t share significant resources. This is how you can both drive a car and listen to a podcast. It’s also why you suddenly need to turn down the music when you need to navigate, or park. Those require use of general cognition, which the music/podcast was using.

An interesting example of this is time keeping. Some people can talk and keep an accurate mental timer. However they will lose track when looking at images. Others will be the reverse, or something different.

It turns out that humans don’t have a consistent time keeping mental circuit. We hijack other systems. If you “hear” the time passing, you will struggle to also hear someone talking without issues. If you visualise a clock, you can talk, but your visual cognition is now occupied.