You don’t choose to eat a birch tree, this is not food, but it is food adjacent. A birch tree is close enough to being food that at the end of winter when you are out of everything and nothing’s fresh, you’ll see greens for your meal in the birch tree first: a gift from the sun to the earth and thereby you, an early edible tribute you badly need.
The shoots and the sap, go for them first. They happen first. The shoots, the tips of the branches, the new green leaves, they’re all nice in a stew and you can eat them fresh right off the tree. It’s a little bitter, but tender and will clear your bronchial passages which you might enjoy after a winter by smoky firelight.
For the sap, stab the birch with something sharp, just into the inner bark. Pull a little bark outward under the wound and let the tree bleed off of that into something. You can get several gallons. It’s the sweetest of waters, nutritious, fermentable into alcohol given time.
Later when the tree produces catkins you can eat these as well for their protein. You will have other options around you by this time of course, the earth will offer you mercy and sustenance.
The birch holds a further secret just under its bark. You might eat it during the lean winter months, forget waiting for spring, by grinding the inner bark into a powder and mixing it into your flour for bread. There is some nutrition to be found here, you can stretch your stores, especially when you are exiled in wretchedness with nobody to turn to and you have nothing else.