why in **** I can't redeem digital code of DVD I got for Christmas into Apple TV?

Did you do as described? Do you have an iPhone, iPad, or iPod touch, Mac, or PC with iTunes?

Redeem digital copies of DVDs or Blu-rays in the Apple TV app or iTunes for Windows - Apple Support

What happens instead? At what point doesn’t it work for you?

Do you get an error message? What does it say?

Does the MacMini support external Blu-ray drives?

Sure. External optical drives with USB are quite common. I have one. Not used much these days, though.

Software is a different matter. You will need player software for Blu-ray movie discs, as the drive is just a reader. No Blu-ray player software is bundled/default install.

Best apps for playing Blu-rays on your Mac in 2021 - iMore

Basically three options, none of them ideal, or even good enough. If you go for movie discs, my advise is to use a set-top player with your TV instead.

I have a curiosity question. Does the MacMini support external Blu-ray drives? If it does that’s fantastic! If it does not why?