This is such a dreadful situation to be in, I’m so sorry.
There just is no good option here, it’s a case of the least-worst option for you and what you feel you could cope best with.
You will hear stories of when doctors got things wrong and of course this does happen in some situations.
A late stage termination would be incredibly difficult for you, as would continuing with the pregnancy. If you choose to continue and see what happens from there, the staff will do everything in their power to minimise any suffering for your baby, but there may be limited options.
I work in my local maternity service and the services for those who are losing / have lost a baby are exceptionally good here. You’d be in a private suite away from the rest of the maternity unit, separate entrance etc, and given all the time you need with your baby.
I think you need some more information from the medical staff involved on what their plan would be if you did choose to continue - would your baby go to NICU (possibly at another hospital far away as it may need to be the highest level of NICU) and would they make attempts to prolong his life, or would they feel this was not appropriate? Would your baby be able to stay with you or would they spend the time they did have in an incubator, with wires and breathing assistance etc? These are things they may not have discussed with you, and understanding what you might expect may help you to make a decision.
I would also ask about how likely it is that they are mistaken about the severity, whether they’d be able to tell this at birth, and what the plan would then be. What sort of care might your baby need, what might you be able to expect longer term etc.
These are such painful things to think about but it may help you to make a more informed decision
There is no right way to handle this, whatever you feel is best is the right way to go.
Sending lots of love to you 