To answer the questions simple and plain, no doubt that most projects will be delivered through significant usage of AI in the future.
Technology has been steadily impacting project management and its principles for decades, with the pace accelerating in recent years.
Though not necessarily being AI, project management, has been embracing a lot of integration and automation technology, and is reaping its benefits.
AI might seem a bit scary, yet it is the logical next step.
Rather than run in fear, let us use and treat it as the technology that is the friendly kind that helps (like Sonny in "I, Robot").
Project management and AI co-existing, with AI being the accelerator increasing project success rates.
In the short term, AI will gain traction quickest in the technical aspects of Project Management.
Especially those already using integration and automation practices, and where significant amounts of data can be collected and analyzed.
Think for instance about business case realization, progress tracking, and risk management.
Tools exist in several industries, that can be amended to work for project management (e.g. risk management tools in logistics), or significant amounts of data can be collected quickly.
AI will support facilitating communication to improve accuracy and increase efficiency.
I don't see AI be the game-changer in the people aspect of project management any time soon.
Those who have strong "soft skills", such as leadership, communications, empathy, and people & stakeholder management, will keep adding real value and drive successful change in project management, for a long time coming.