I think it is very unrealistic to expect carbon capture technology to ever compete with growing trees.

I don't understand this point. Do both.

Doing it synthetically uses up a lot of energy so doing both would potentially diminish the natural way’s efficacy.

Why is it unrealistic to build carbon capture technology that is much more efficient at carbon-capture than trees?

Trees aren't optimizing for carbon-capture, so they're probably leaving a lot of efficiency on the table.

I don't know what you mean by efficiency but trees grow on their own while whatever technology you use for carbon capture will need an external energy input. If we have trouble meeting current energy demand with carbon free energy sources then we will have even more trouble if we increase energy demand even further.

Trees may not be deliberately optimized for carbon capture, but they really aren't much more than maintenance free, solar powered carbon sequestration machines. Most of the mass of a tree is carbon that came from the air.

When 1% of the permafrost melts per year, it releases about as much carbon as all of humanity combined. Where would you get the energy from to suck that back out of the atmosphere? Who would pay for it?