Yes but photosynthesis doesn’t generate energy but the opposite: it takes in energy from the sun in order to reverse the reaction
You have to pick one. CO2 removal or creating energy. If you remove it, it must remain sequestered. If you create fuel from it, the CO2 will not have been removed.
I'm not against the idea of sourcing fuels from atmospheric CO2. It's a good way to get energy-dense fuel without adding new carbon to the atmosphere (assuming a carbon-free source of energy is used to synthesize the fuel). But that process won't remove CO2; it'll just not add more.
The problem isn't technology, the technology for genetically modifying alge or bacteria to consume CO2 and produce oil has been around for quite some time.
The problem is our powerstructures and our economic investments. It takes tremendous energy to move such a massive Goliath of a ship.
Our economy which brought us prosperity simply cannot move quickly enough to prevent our demise. Ironic and perhaps poetic really