I think that economic output is the sum of a lot of other curves. All exponentials come to stagnation pretty fast when they hit their limits, but in our history whenever that happened, there was already a new summand added to the economy which starts a new exponential growth.
Many of the curves improve factors of things that don’t grow any more. For example, many wealthy nations don’t have population growth any more, but still increase per-capita output. Likewise, many nations don’t have a growth of the energy input, but they’re using energy more efficiently.
Machines (and energy transformations) have made it possible to decouple economic output from the physical labor of humans and animals. Electronic communication (starting with telegraphy before there even was electricty) has decoupled the transfer of information from the transfer of matter.
Electronic data processing (and AI) decouples one more thing from the need for biological brains. Even without AI, modern software does a lot of work that we already wouldn’t have enough humans to do!
Maybe one reason for the economy to have been growing over so many different epochs is that the definition of what an economy is has expanded to include more and more things, which previously didn’t exist.
With every task that machines took over from humans, humans found new tasks to create and sell even more things. And the more basic needs are taken care of, the more we focus on entertainment, status, and great projects of humanity like the settlement of Mars, and extending human lifespans. Maybe it will be during our lifetimes that machines take care of all the basic needs and humans will only care about entertainment, their social relationships, and the great projects of humanity. And many, of course, will already be satisfied fith the first two of those three points.
Addendum: a great “decoupling” event was when countries stopped tying their currency to precious metals (or indeed anything material) … first it started by introducing paper notes, and now money can exist just as an entry in a bank account. If the economy is just numbers of money then this decoupling means that the economy than grow higher than the number of atoms in the universe which is often cited as a hard upper limit.