We don't know for sure of any planets around Alpha Centauri but, if there were any, SPHERE should be able to resolve a 5000 times fainter (the system is 75 times closer) IR source orbiting as close as 2 UA (roughly the same angular separation from the star as the closest planet detected at 160 UA) from Alpha Centauri A or B.

As for Proxima, Proxima b orbits at 0.05 UA (which is very close). I don't think we could separate its light from the parent star.

Alpha Centauri has a binary system with another third sun orbiting the other two at half a light-year or so. Not very "sun-like".

However, it has planets thought to be in the Goldi-locks zone around one of the stars. Seems like if they can get that kind of resolution at 300ly, they should be able to do infinitely better at 4. Just a thought, I am sure I am missing something.

A comment upthread mentions that one of the biggest obstacles to detecting planets is the huge contrast between the planet and its host star: detecting 10-14 orders of magnitude difference between the luminosity of a star and orbiting planet cannot be made simpler by adding in 2 additional stars.

Another commenter said: "The two gas giants orbit their host star at distances of 160 and about 320 times the Earth-Sun distance."

Just a guess but perhaps being in the Goldilocks zone the planets are harder to discern from Alpha Centauri.

I figure the technology that blocks the star light may mean this isn't the case though.