The planet is about 0.05 AU from Proxima Centauri, meaning we need an angular resolution of about 1.9e-7 radians to even distinguish it from its host star. Is that realistic?

In theory, an orbiting space telescope has a diffraction-limited resolution of approximately 1.22λ/D (λ = wavelength, D = aperture size). Modern image processing techniques can improve on this somewhat, but it makes a good order-of-magnitude estimate. Anyway, this formula tells us a 4-meter telescope has a maximum angular resolution of about 1.8e-7 radians at a typical visible light wavelength of 600 nm. That would be just good enough... except that we don't actually have a 4 meter orbiting space telescope. Resolving even large features on the planet would require a much larger telescope, probably kilometers or more.

For ground based telescopes, the situation is even worse because of atmospheric effects. Despite being 10 meters in aperture, the Keck telescopes in Hawaii are limited to an angular resolution of about 2e-7 radians because of the atmosphere. However, there is reason to hope that the even larger European Extremely Large Telescope will have enough resolution (about 5e-8 radians? hard to tell from their official publications) to image Proxima b directly. https://www.eso.org/sci/meetings/2011/VLTI2011/presentations... Again, this is still not enough to resolve surface features.

So, long story short the answer is unfortunately no at present. Maybe space-based manufacturing will let us build a big enough telescope someday?