Is there any way to have my computer automatically change timezones as I pass them while on a flight?

Technically, a time zone changes 1 hour every 15º of longitude -
Then you would have to enter your GPS coordinates -
Of course for practical reasons, they most often follow actual borders of nations -
Then some nations include daylight savings variations to complicate things...!

My wristwatch does that, but I know when to change the time zone -
Look the Seiko M158¨Worldtimer -

There is no way to set your computer to change time zones on a timer or any time-based format. The computer will usually reset its timezone when connected to the internet.

My phone does that by itself when I land

Not on the flight, as most don't allow the use of phones and computers at the moment. On the ground, some computers may update to local time, it depends on the ISP the local zone is using.

unlikely most apps and the like use the internet for the data, and that is out of the question obviously.

No. The location awareness that automatically sets the time zone won't know where you actually are other than that you're on the plane.