Was it definitely a CFP that arranged the network build in the area ?
If the area was provided with a CFP ( community funded project ) that’s really an Openreach initiative, and once it’s completed there is no obligation to use BT ( but those that made a commitment are expected to take the newly provided service from someone ), you say your name was on this list, but that’s not really how the process works , you would need to have contributed financially to the CFP , as your neighbours did, either directly with your own money or with a government voucher if the area was within the scope of the ‘Gigabit voucher’ scheme, unless a benefactor provided the entire ‘public’ contribution towards the CFP.
If ( for example ) your immediate neighbours to the left and right both committed to the CFP then obviously they are included, but a property’s in the middle of them , even they didn’t commit to the CFP, is likely still covered, however a neighbour that isn’t particularly close may not be included , or if they were not within the scope of the project initially , or were asked to participate and refused and ended up outside the boundary of the CFP , that’s just how it is.
If this is CFP is overhead ( telegraph poles ) then the FTTP apparatus is visible ( a CBT , connectorised block terminal ) and if the pole that currently serves your property with a copper line also has a spare port on this CBT , then FTTP should be available, if the area is served underground then it’s not as easy to tell.
As already asked, perhaps you can show the checker returns for both your address and your nearest neighbours, with an indication of how close the neighbour is, some in rural areas may consider someone a neighbour, even though they are 100’s of metres away
