I am afraid there would not be any Manhattan like projects the fear of the enemy being the first in creating a powerful entity like agi would impel them towards total annihilation of the other

unless there is a huge recession or world war III sets in I don't think improvement is likely to stop

either there is not much you can do in case ai becomes powerful enough to solve most of our problems(just enjoy utopia unfold) or if anarchy hits having a strong network of friends will be crucial so i would try to expand my friend group, cooperation has always been vital and those with better networks were the ones who came out on top throughout history you see even if you were a billionaire with a bunch of land, resources etc, the one determining factor of your survival would be your social status, how many people you can work with and how reliable they are under hectic circumstances so the bottom line is have a strong network of friends who you can trust with your life will be quite advantageous

give it another 10 years and software writing ai may easily replace the average engineer

Higher order work will probably still be handled by humans and time spent on lower level tasks will be passed over to ai. Instead of needing 10 people on average for a project there will likely be 2-3 programmers left with an ai assitant.
The current boom in the number of software engineers will contribute to the advancement of these ai assitants providing them with unprecedented amount of data.