The obsolescence of life cycle analyses is a topic in itself, and the lack of accessible data is a problem for anyone who tries to investigate high-tech products.
For the solar powered website article, it's the order of magnitude that matters. You say I overestimate the energy use of solar panel production, but in our configuration it corresponds to just 1 liter of oil per year.
You can get a reasonable estimate by taking the wholesale price of the thing you're analyzing, dividing by an average price of electricity for industrial use (like, around US$60/MWh, in the quaint non-SI units traditionally used in the trade), and multiplying that by some fudge factor like 20% to account for the fact that much of the cost of things is due to non-energy inputs like raw materials, skilled labor, and interest. This gives a result correct to within a factor of 3 for the vast majority of goods and services, while using LCA numbers from a quarter century ago did not. In this case the result is 2.3 MJ per watt (peak) of low-cost solar panels using €0.17/Wp from PVXchange and SolarServer. That's almost an order of magnitude lower than the 22 MJ/W you used in the article (assuming 16% efficiency; with 21% efficiency it's 16.7 MJ/W. I'm not sure which one your original number was for.) So I think you may have gotten within an order of magnitude, but only just.
If the numbers you were using were correct, then just the energy input for the solar panels would have cost more than the wholesale price for the modules.
Calculating embodied energy based on costs is an option, but I have always learned that it's the last resort, as it has many problems, too.
For example, How do you account for the fact that all production facilities for solar panels have moved to China? If you look at the price evolution of solar panels, there's a gradual decrease due to technological progress (less energy use indeed). Then, from 2009 onwards, the decline in costs accelerates sharply, the consequence of moving almost the entire PV manufacturing industry from western countries to Asian countries, where labor and energy are cheaper and where environmental restrictions are more loose.
The manufacturing shift to China can account for a one-time step decrease in solar PV costs due to lower wages and a lower cost, dirtier industrial ecosystem (e.g. high-CO2 grid power supplied mostly by coal plants having minimal pollution controls).
But the costs of solar panels made in China in 2020 are much lower than those of solar panels made in China in 2010. Chinese factory wages have not fallen over the past 10 years, nor have Chinese pollution controls been further relaxed. The trend of falling costs over the last 10 years of made-in-China solar panels is due to improved techniques of production.
In 2010, Chinese producer Suntech was the largest PV manufacturer in the world. It sold 1.6 GW of panels and realized revenue of $2.9 billion:
This 85% drop in prices indicates that technological and manufacturing progress in the solar sector continued at a rapid clip even after its center of gravity shifted to China.
Agreed that it's a one-time step decrease, and that the progress continues. But, why 2020? The panels that have powered the server were bought between 2015 and 2019, and who knows how long they had been in storage before I bought them.
You take the solar panel that just comes out of the factory as a reference, but I could just as well argue that the reference should be the age of the average solar panel installed in the world.
Also, let's wait and see how the move to China affects the quality and life expectancy of solar panels. And what it means for other forms of pollution. I focused on energy use but there are other environmental concerns with the production of solar panels.
I will be happy to update the calculations in the future if more and better data are available.
For the solar powered website article, it's the order of magnitude that matters. You say I overestimate the energy use of solar panel production, but in our configuration it corresponds to just 1 liter of oil per year.