Note that Openreach is the BT Group company that provides the exchanges and the actual connection network. Within each exchange a/your connection can be connected either to BT Wholesale or the ISP's (in this case Zen) own onward/receiving backhaul to Zen's in-house routers and servers.
Lift and shift on FTTP I'm not familiar but expect it is similar in effect to on FTTC, where your connection goes through different physical ports on the Openreach and other equipment in the exchange. Or perhaps the distribution port serving your premises.
I dunno!
If it goes via BT Wholesale Zen has to connect into at least one of BTW's 20 nodes to collect or send the traffic. If it goes via Zen's own backhaul, (fibre rented from some other network provider) then it tends to be far cheaper for Zen than using the BTW service.
However there is no escaping the Openreach physical connection between you the subscriber and the exchange unless one of the newer companies such as CityFibre has cabled your street. (And of course Virgin Media which has been around for decades but is a different technology). If with one of these new companies or an ISP that uses them then Openreach are not really involved in the day-to-day stuff.
Connections: OnePlus 8 Pro on Three 4+ (LTE)/5G and at home Three Mobile, with (Three)ZTE MF286D router giving about 113/20Mbps.
The best of all possible countries.