We always used the Yoyo with car adaptors & the Cybex Cloud Z car seat which goes near flat. x
Our cybex gazelle pram lies flat and can be used either parent or world facing. It is part of a travel system but you can buy it separately on its own too x
I'm afraid what you're looking for doesn't exist! In order to be parent and world facing the seat needs to be detachable from the frame and sit inside it, this makes the frame a lot wider than most travel strollers. There are some completely flat travel strollers. Have a look at Joie pact, silver cross clic and joolz aer
I got the bugaboo bee for holiday, doesn’t fit in cabin, but folds flat and goes rear and forward facing!
Not Rear facing but we have the zummi Eden compact stroller and it fits in the cabin and lies completely flat. Has a great shade aswell. We also bought a snoozeshade to cover Baby whilst napping or in high uva
https://thelejouxstroller.com/products/lejoux-baby-pushchair?variant=44311557112025
The Lejoux that Ezgi linked is probably the best bet! I don’t think it’s cabin approved but you can check them in at the gate and then just pop little one in a carrier for boarding the plane and waiting for luggage the other end x
The Nuna Mixx Next is parent and world facing, plus nearly lie-flat. It can be folded with the seat attached and can buy as just the stroller rather than a travel system. It's not particularly small/compact so probably not cabin approved but most airlines let you take buggies up to the gate then put it in hold (some airlines you can then pick up at the gate the other side or it comes out baggage hold). I'm planning on looking for a cheap second hand buggy for when we go away so it doesn't matter too much if gets bumped about in hold.
Thank you everyone for taking the time to respond! I’ll look into all your suggestions 😘
We have the silver cross jet 3, got one of fb market place for next to nothing, rear facing, lies right back and fits in the hold 😁
@Jodie jet3 is forward facing, not rear?
We used the chicco echo that lays flat but I just unzipped the hood so I could see her all the time as she was only 9 weeks when we went away
Barely any strollers lay completely flat, and I don’t think any rear face. This website is helpful https://www.independent.co.uk/extras/indybest/kids/pushchairs/best-compact-stroller-a9413806.html