There is a cyst on my left ovary, though it's smaller than yours. It was found at the 12 week scan and noted, at the 20 week scan they had to go look for it as it had been pushed to the side, but it was still there, roughly same size.
For me there were no consequences apart from "If you develop strong pain (and it would be really very bad pain) then go see someone immediately, but probably nothing will happen."
No further scans booked, no further observation of the cyst.
I gather ovarian cysts during pregnancy are very common. That's probably why your GP said not to worry about it.
BUT my first sonographer also explained that there are cysts and cysts. Mine was completely clear - just a black space on the monitor, no "clouds" inside. Apparently these are "good" cysts with little cause to worry. But there are others, and the good ones can develop into bad ones, thus the need for monitoring. The bad ones could for instance twist and somehow cut off blood flow (I can't precisely remember what the sonographer said) and that would cause intense pain and potentially harm the baby.
So I'm sorry to say but if your sonographer/consultant thinks your cyst is worrysome and needs monitoring, then he/she is probably more informed than your GP who just goes by the "most cysts are harmless" rule of thumb. On the plus side, it could still turn out to be nothing to be worried about, and the additional monitoring is just that - checking to see how it develops.
Hoping it all turns out well for you. Do keep in mind - your baby is healthy, and even if it should be a problematic/malign thing, it is not a terribly bad thing to happen - it can be dealt with; it has been picked up now and will be monitored. Good luck