I’m entitled to social broadband with other company .
I have had my BT TV Box since 2019.
if I keep my box with I be able to view and record on it
A BT TV box with youview interface will operate as Youview box so standard ( non ISP players) and Freeview aerial delivered channels will be receivable and recordable.
Ownership of the box will depend upon when in 2019 you received it.
The key date is 13 December 2019 so if you got it before then it's yours to keep regardless of what Customer Services might tell you at any point.