It is currently fashionable to assume a miraculous Singularity AKA "rapture of the nerds" that will magically transport us past economic and materials limits. I am not convinced; the more Real Science I learn from conversations with working scientists, the more holes I find in Kurzweil/ Drexler extrapolation.
We will reach the stars in the far future, but we will spend millenia spreading into the solar system first. Industrial civilization uses less than 20 TW of power. The Sun emits 400 trillion TW. The black body temperature of a 50 AU shell is around 60K. This suggests we can use 20 trillion times as much power 5 times more effectively when our bio-engineered descendants spread to the Kuiper Belt.
Too much of our future thinking is channeled by penny-per-word pulp science fiction. Pulp writers can type "light year" faster than "astronomical unit". Hence a Darwinian advantage for writing about interstellar travel. However, Proxima Centauri is 25 million times further away than the Moon, the farthest place humans have ever visited.
The current Moore's Law rate has dropped to a few percent per year, about the same as the 3.5%/year growth of gross world product (they are related). So, extrapolating to the stars at 3.5% per year (assuming we reach the Moon again Real Soon Now) is 500 years of continuous compounded growth.
However, the 3.5% growth rate is predicated on a speed-of-light information economy supported by speed-of-sound material flows; a solar-system-scale civilization will innovate faster (more innovators) but expand slower physically (slower information/material cycles than a compact globe).
So, I think we are back to millenia-to-the-stars.
Note that we set a record for interplanetary launch speed in 1945, when Fritz Zwicky launched ball bearings into space with the Trinity blast. Ball-bearing-mass light-sails to the stars are NOT useful star probes. Gynormous zero gee observatories are, so we are back to keeping space clean to protect optical surfaces.
That's not what science fiction fandom wants to hear.