I don’t believe VGA supports 1080p by default, at least according to Batocera. You could theoretically get up to 1270 horizontal resolution at 60Hz but going higher would involve custom resolutions that lower the Hz (down to 30Hz for instance) or reducing the colour-depth. Both of these things are very technical and not recommended for the average user to attempt.
Coincidentally I’m working on a Batocera-on-CRT guide with another dev at https://wiki.batocera.org/batocera-and-crt which might give you some more insight, if you like a word-y explanation of things. That guide focuses more on converting digital to analogue, not analogue to digital like what you want to do.