there’s a script for anti-aliasing: GitHub - rikfuzz/aseprite-scripts: Scritpts for Aseprite
it can be easily changed to support alpha as well.
however it works only for two selected colours (foreground and background) at once and the results are more ‘good start’ than ‘one click solution’.
somewhat good news is the fact this is planned feature: Antialiasing filter - #2 by dacap
but so far it has been moved to v1.4.