[nurettin]

If you watch any Hikaru Nakamura content, you will see him draw "classic right angle triangle"s with three pieces, "classic wooden shield"s (a cross showing the scope of a centralized bishop), so he definitely uses some kind of geometry while playing.

Not sure if he just recognizes the shapes as they appear or tries to make them appear, would be nice if he came here to answer.

[chatmasta]

This is called “chunking” [0] — identifying grouped assortments of pieces as a single semantic unit - and has extensive research [1] behind it.

[0] https://www.chessprogramming.org/Chunking

[1] https://pmc.ncbi.nlm.nih.gov/articles/PMC4361603/