Well you can do the maths.

Let's assume it takes 1 year to pay back the energy usage, on average, for the green projects (look up that Wikipedia link). Let's also assume that we can dedicate 5% of the world's energy budget towards new power plants and that the world stops growing. So: 5% energy recession and zero global energy demand growth. How long would that take to roll out? 1/5% = 20 years, all of those years will be of serious austerity. Multiple countries (especially those with "good", that is growing demographics) would blow up. Up to you to decide if it's feasible to execute, and those are very optimistic numbers. What if the energy usage grows at 2% and we can dedicate only 3%? Well, that would give us 1/(3% - 2%) = 100 years to finish the project.

These are not happy things to look at. Personally I'm just trying to avoid the impending climate doom. Whatever happens - this problem is here to stay with us for many decades.

That's some weird kind of fear mongering. You assume instant replacement of fossil fuel plants. If you don't do this, but keep them running, and add renewables on top, it looks different.

Using your numbers to demonstrate it of 1 year EROEI. Let's say we make a starting investment for one year where we take 5% of the world's energy output to invest into new renewable power. After that year is over, we have capacity to generate 5% of the world's energy output per year, but we don't replace any of the existing fossil plants, but put it to work for new energy plants. So the second year we spend that energy on another 5% of renewable energy. Now we have capacity of 10% of the world's energy budget at start of year 1. If we continue doing this, we have 20% after the third year, 40% after the fourth, and 80% after the fifth. By the end of the sixth year, we can generate 160% of the energy demand of the world at start of year 1. We can now turn off the fossil fuel plants and enjoy a 60% increase in energy output, most likely more than the world has grown in that time.

Now you wonder, won't it cost tons of money to use all of this energy to build new plants? Sure it will, but that's already priced into things. That's what we have banks for.

Your fears are unfounded.

You're right, I did not compound the green energy (or, as you say, assumed parallel termination of dirty plants). It would work if the world could collectively put aside 5% of the energy budget. Not sure if that's realistic, and also will there be enough commodities (though those are at multi decade lows in prices right now), but if so it should work.

Let's see how the world looks like post covid, as we're very likely to experience a huge "energy recession". Something that would be similar to that 5% energy austerity rule.

We have tons of unused capacity. Energy shortages would be indicated by high energy prices, but they are low. China had been building coal plants before actually having demand for them (creating a great place to mine BTC in the process), then expanded to build coal plants all over the world. The US is swamping international markets with fracking oil. In OPEC, the hate for each other still seems to be stronger than the desire to increase prices.