Is our universe expanding? Or does it only seem bigger because our ability to look further into the universe has grown?

Cosmological expansion is driven by dark matter, as evidenced by the observed separation of galaxies, which is maintained by gravity.

It's not a matter more and more powerful telescopes seeing more and more distant galaxies. Instead we measure the expansion of the Universe from the spectra of galaxies showing a red shift -- the galaxies are moving away from us and that causes the light from the galaxies to be stretched out to longer wavelengths and lower frequencies. The red shift is what shows the expansion, not the absolute distance.

See:

1. The doppler effect for how moving objects lead to waves having a different frequency: https://tutor.hix.ai

2. How this effect is seen as a red shift when galaxies move away from us: https://tutor.hix.ai

The observed redshift of distant galaxies, which shows that they are moving away from us, confirms that our universe is expanding. This expansion is not caused by our ability to observe farther into the universe; rather, it is an intrinsic property of the universe itself.