It was openreach who installed the ONT not BT RETAIL
Are you currently a BT broadband customer or with another ISP?
The Ethernet cable is your responsibility, you need to get a local tradesmen to do it if you don't feel capable of doing it yourself
The easiest way to route and hide an ethernet cable is to get use a flat cable that you can almost invisibly tack to skirting boards.
If you can't install an ethernet cable without major disruption or unsightly results it might be worth looking at Powerline adapters. Not sure if anyone has tried them between the ONT and router, but since the connection is Ethernet should be worth trying at least (just make sure you can return them if required.
Powerline adapters between the ONT/PON and the router will work, but you'll need to test them on the LAN first to make sure you have the throughput. Once they are on the WAN side it's difficult to see the connection stats (sync speed and throughput can be vastly different).
I’m with BT I had bt broadband and phone installed over a year ago, I’m not sure if it was a bt or OpenReach person who installed the ONT box
I need to move the ONT box and bt router from one bedroom to another, so I should contact a local tradesman or OpenReach