I think a silver birch, though lovely, would not be a good idea so close to your neighbours, even if you hate them! It would eventually grow too large for the space, though admittedly that would take a while, but in the meantime it would not be much good in terms of shade or privacy.
I would put up something like a very basic pergola and grow summer flowering climbers up it, would give you some privacy in the summer months when you are likely to be out there ,and some shade and some scent depending on what you plant.
Avoid anything marked “good ground cover” on the label.it is garden speak for thug that you can never eradicate..
For ground over I would try some of the tougher geraniums for a start . Some ferns could be happy there too. Try Googling “dry shade “ plants and see what comes up.
To encourage invertebrates why not make a bug hotel? You can buy small ones but you can also make your own with old logs, bricks, concrete slabs etc layered up and filled with cut down canes, old books, corrugated cardboard, straw.......... again lots of ideas on google/Instagram.