Population projections lose a lot of their accuracy when they start dealing with people who have not been born and guessing at the rate at which they will choose to reproduce. Population projections are far better with calculations based on counting who is living now and figuring that the people who are fertile now will reproduce at the same rate as other people in their same generation in the same country and region.
The main medium projection is for population to go to about 9 to 10 billion around 2050. However, if fertility rates increase slightly and death rates were to drop then the population could continue to grow.
There is plenty of technological improvement which can manage this situation and enable everyone to be wealthy and healthy.
Energy can be provided with mass produced deep burn nuclear fission, nuclear fusion and space based solar power.
Molecular nanotechnology, additive manufacturing can enable more efficient use of material resources. The US military and Airbus and other companies have active funded projects developing additive manufacturing
The solar system and its resources can be unlocked over the next 10-40 years. There are various technology paths to spaceplanes or other technology to resolve the issue of getting to earth orbit. Solar electric sails, plasma rockets and other propulsion can open up movement throughout the solar system.