How does fuel economy quantitatively depend on altitude for a jet?
I am adding this community wiki answer to show my current state of research and to provide the plot vs. altitude, which I will update when I learn more. Comments are welcome.
Thermal Efficiency
From this answer by Peter Kämpf, we know that the thermal efficiency for jet engines is given by
$$ \eta = \frac{T_\text{max} - T_\text{amb}}{T_\text{max}} $$
where $ T_\text{amb} $ is just the ambient temperature (from ISA) and $ T_\text{max} $ is the temperature resulting from the combustion. If I understand the answer correctly, this should be about 1100 K above ambient temperature, so I am currently using this term to describe the impact of thermal efficiency on fuel economy:
$$ \epsilon_\text{T} \propto \frac{1}{\eta} = \frac{T_\text{max}}{T_\text{max} - T_\text{amb}} = \frac{T_\text{amb} + 1100 \, \mathrm{K}}{1100 \, \mathrm{K}} $$
I am not sure if the increase in temperature of 1100 K is constant with altitude, so please correct me if this is wrong.
Drag
From another answer by Peter Kämpf, we know that induced drag is proportional to dynamic pressure
$$ q = \frac{v^2}{2} \cdot \rho $$
with $ v $ being the TAS and $ \rho $ the density (known from ISA). Since work required to overcome the drag per distance is proportional to the force, the fuel economy should just scale with
$$ \epsilon_\text{drag} \propto \text{TAS}^2 \cdot \rho $$
Propulsive Efficiency
From this answer we know that the propulsive efficiency for a jet engine is given by
$$ \eta_p = \frac{2}{1 + v_e / v_0} $$
where $v_e$ is the exhaust velocity and $v_0$ is the TAS. As far as I could find, there is no straight-forward way to relate $v_e$ to altitude and temperature. For the moment, I added the propulsive efficiency for a high-bypass jet engine from the following plot from Wikipedia:

(image source: Wikipedia)
Summary
For the combined (relative) fuel economy term, I just multiply all previous terms:
$$ \epsilon = \epsilon_T \cdot \epsilon_\text{Drag} \cdot \epsilon_\text{Prop} $$
The following plot now shows the relative fuel required per distance. Each curve has been normalized to 1 at sea level.

The propulsive efficiency dominates as long as the TAS is increased. Afterwards, the lower drag dominates. The overall fuel use is almost half as low at high cruise altitudes compared to sea level.