These things are engineering marvels as fuel-burning engines go. From what I know, there is actually not that much that can be done to make gas turbines more efficient if weight is no object. Fuel weight and cost are very important for commercial turbofans, and engine manufacturers have been doing a huge amount of R&D in efficiency and are using some very advanced manufacturing techniques for certain parts. Turbine inlet temperatures are well into the white-hot range. A mechanical engineer described it to me as "A hundred degrees hotter and they'd melt and spill their internals out the back" - that is with exotic metals and active cooling. The main problem with these turbines is that they are somewhat old and will probably run at less than maximum power for longevity reasons. Turbines are terrible at less than full power efficiency. They also won't have a steam turbine added to use the exhaust heat like with stationary engines.

According to this article, the best current commercial turbofans can reach over 50% thermodynamic efficiency. I remember thinking that 50% seem like an unreachable holy grail when first reading about thermodynamic efficiency of common engines. https://nap.nationalacademies.org/read/23490/chapter/6#36