Is this video a legitimate way to get Linux on LineageOS via Termux or is there a better recent method?

If you got root, running a Linux container under chroot is faster than proot so use that instead.

And if you want a full blown Linux distro then Ubuntu touch or postmarketos it is. Look into libhybris if you want your own distro on your phone

I had plans on testing a dualbooted Linux/Android setup by reflashing the boot partition every time I wanted to switch but haven't done it yet