It always puzzles me when people think fusion is just infinite free energy. You're not just gonna have one fusion plant producing a billion zetawatts of electricity. Each fusion plant will likely produce roughly the same as a large nuclear plant. So we would need to build hundreds/thousands of them, it would take many decades to build them. Fusion reactors are extremely complicated machines.

And even if we did this, we would also need tens of thousands of carbon capture facilities, and the infrastructure to actually store the CO2 somewhere.

Carbon capture (from air) is just completely infeasible. It's not even remotely realistic. There is absolutely no way it will ever make a significant difference.