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?
Much more than that; that's the angle for HALF-maximum brightness, but since the star's many orders of magnitude brighter than the planet, you'd need a much larger reduction than 1/2. Unfortunately, the diffraction-limited pattern [0] has fat tails -- it's not Gaussian, the brightness is slow to drop off away from the center (polynomially slow? [1]). I understand you'd need >100 times the FWHM angle in practice, on the order of 1" for JWST for instance [2]
This is why coronagraphs will be so useful.
[0] https://en.wikipedia.org/wiki/Airy_disk#Mathematical_details
[1] a log-log graph shows the envelope is close to inverse-cubic (x^-3)
[2] http://nexsci.caltech.edu/workshop/2016/NIRCam_Planets_and_B...