The BBU that was fitted alongside the ONT on early FTTP installations was Openreach supplied ( not BT ) , FVA was available to other supplies not just BT but no other ISP bothered with it, especially as the copper pair service could be maintained ( if it were required)
DV is a proprietary BT service ( and nothing to do with OR ) , so references on a BT site to a ‘BBU’ are presumably about BT supplied BBU/UPS ( a UPS is a essentially a battery /inverter)
BT will supply some customers that qualify with a free UPS , others , if sufficiently worried can purchase one themselves ( when in stock ) from BT, or something similar from various other retailers.