Wouldn't land-based telescopes already use larger mirrors than any space telescope?

Yes they do, but you have to consider the problems that the atmosphere poses. A lot of the budget for ground telescopes goes into the adaptive optics (actuators that can deform the mirror to compensate for distortions due to non-uniform column of air above the telescope). For adaptive optics to be effective you need bigger mirrors because you can't deform a small mirror enough to counter that.

Additionally, the atmosphere blocks a bunch of wavelengths that are really interesting to observe [1] so we still want to be in space for these observations.

Finally, in the non distant future I believe space telescopes will ditch mirrors altogether. For instance, the proposed Aragoscope [2] would use diffraction optics instead of so called geometric optics (lenses, mirrors) to focus light. Since the material that can provide the diffraction can be anything it would be much cheaper to launch a sheet of <insert light and bendy material here> that can unfold once in space instead of incredibly precise and fragile mirrors. Also, according to Nasa, this approach can achieve ~1000 time the resolution of HST at a fraction of the price and we are only limited by the size of the disk creating the diffraction.

[1] https://www.researchgate.net/figure/The-atmospheric-transmis... .

[2] https://www.nasa.gov/content/the-aragoscope-ultra-high-resol... .

Can you launch those mirrors into space on a rocket without them turning into very fine glass dust? Cuz I bet a lot of mirrors in land-based telescopes would simply shatter or break on a launch.

Haven't a clue. It's an interesting question. What kind of materials they're made out of (weight considerations?), what kind of forces they can take, what kind of support structures they require, etc.

why not build the mirror in space? I bet microgravity could help with some of the challenges of building one.

It is going to take long while to build infrastructure to support any kind of construction let alone high tech construction like this.

Also I don't know if there actual benefits in doing mirror construction in low gravity