No we don’t have to, great answer for vegans I guess!
So what is the replacement then? You heard the bell rang, that’s right: Yoghurt! When you are cooking your borek, if you do not want to use egg or if you have ran out of eggs, spread some yoghurt on the top layer of the filo pastry, then add your blackseeds or anything you like as a topping. Easy as that!
Also there are options in vegan shops like egg replacement powders, but personally I don’t like using those.
Another alternative is grape juice syrup or grape molasses. You can find them easily in Britain.
Have a few spoonfuls of it in a bowl and make it thinner with some water. Spread it thinly over your borek and it will be roasted beautifully!