Total biomass actually peaked 540 million years ago, at the end of the Proterozoic era. See Figure 2 (on page 88) in Franck et al.: Causes and timing of future biosphere extinctions.

Link: https://www.biogeosciences.net/3/85/2006/bg-3-85-2006.pdf

But this is the problem of exponential growth - you can sustain it without even noticing the detrimental effects, until suddenly you can't.

The resource usage of all the doubling time periods until the last one would have used up only 50% of the resources available(this could be millions of years, depending on the exponent), and then suddenly the last one would use up all the resources left.

This is repeatedly exemplified in Professor Allen Bartlett's talk "Arithmetic, Population and Energy"(video link at specific point: https://youtu.be/sI1C9DyIi_8?t=1337 transcript: http://www.albartlett.org/presentations/arithmetic_populatio...)

Except that it doesn't. There are no forms of life on earth that have been growing exponentially for millions of years. Sooner or later growth and expansion always hits its limits and populations stabilize or decrease.

Not really. Moore's law refers to the number of transistors that can fit on a die, and GPUs/TPUs haven't increased that.

What aspect of life on earth has been growing exponentially for millions of years? I'm not clear on what you mean here.

> see life on earth

Notice how life on earth is plateauing...