The first thing I will say is that the smaller / lighter, more compact the stroller will be, the worse the performance with the buggy board, and personally I would not recommend the Bee at all for old town nor with a buggy board for everyday use.
About lie-flat, it is not necessary, it is a thing some people want/need because they prefer it, but others prefer the shaped bucket seats. As long as for the first ~6 months the baby is in the lie-flat mode in the carrycot, you can pass to the ergonomic seat as well as a lie-flat one, and the preference of the baby, you, unfortunately, have no way of knowing beforehand, but I believe if you don't feel bad about your choice, the baby will most probably adapt to whatever you chose.
I think the Nuna Triv Next is a better choice for its sturdiness, if I take the buggy board into consideration especially. There is no way it wil last until 22kg though, space-wise all the reversible models are simply limited in space and if you don't pick a BIG one, the child will most probably use such a reversible seat until about 2-2.5 years of age, and this si something you should count on. The second-time mums, if they want something to last the whole time, go for non-reversble models, knowing they lose the ability to face the child but also knowing the seat will last longer. It's not a bad thing, the smaller seat, as reversible are always bulkier and about those 2 years of age, you will want something simple and small anyway, especially if your child will want to walk more than sit.
So, I would either suggest the Triv Next, or something similar, e.g. the Joolz Hub. I would count on changing later on with that. Or I would go for something facing only forward + a car seat / carrycot option, like a Baby Jogger City Mini2 / Oyster Zero (Gravity) to have to last, room-wise.
Lastly, about the breathability, I wouldn't only concentrate on those that marketing-wise promote mesh and so on (btw, Cybex Mios is a good option for that), you will limit your choices a lot. You can always get accessories - Aeromoov seat liner for the summer, extra sunshade and so on, so yeah, keep it in mind and pick strollers with nice materials, but don't search for only summer strollers, anything can be modified to suit that better with accessories.