What makes a Linux distro portable?

Lots of tiny details, if your grub works fine (which is easy to solve but has a huge direct can't boot impact).

If you use default settings for boot processes, then usually you're fine, since udev will load proper drivers for all kinds of devices, except for those super uncommon ones(not having a kernel driver installed on the disk).

Xorg need some sort of user mode DDX drivers provided by xf86-video-xxx, which is not installed for new graphic card.

The real hard to solve problem is configurations for upper layer applications, like you has a script with hard coded device names. Camera apps use hard coded camera device name. Network service use hard coded device names which doesn't exist any more or you no longer use wireless network anymore etc. Your IP changed, so some internet services may refuse to accept your cookies and require you to re-login.

Anyway, I think if you use default distro settings and successfully boot on your new computer, and Xorg works fine, you can shot not working anymore problems one by one, don't need to solve them until you find them.

PC is made of so many different parts mamufactured by so many companies, there's no neat solution to write a script to switch to new PC. You need to use portable configuration as possible to make your OS portable. That's how PC OS is designed.