currently I have Bt sport and HD extra. I can’t remember how long I’ve had the box, must be years it’s one with two lights at the front.
Typically the new promoted flexible BT TV packages do have a DTR 4000 box provided (loan basis) . Your existing Box would have been supplied under pre December 2019 terms so would be your property. So if you ceased your legacy BT Tv package and took out for example the BIg Sport Tv package plus HD addon you would have the loaned box for your BT subscription use and you could use your old box in another room. Bt offer an Extra Box service c £5/month that allows use of the BT services on a second box at additional charge. You may not need this if you have access to the BT Sport and Now Tv Apps on your second TV.
Note that in moving from a legacy TV package to the new flexible TV packages you are taking the channels and services that are available on the new packages and entering into new minimum term BT TV and broadband contracts.