How can I update the figure counter ignoring the figures with `supplement: none`?

It does change the things. The context is providing the smallest possible code samples.

#import "@preview/subpar:0.2.2": grid as sgrid

#let trans-linear(caption: none, column: 60pt) = sgrid(
  columns: (column,) * 3,
  caption: caption,
  figure(rect[left]),
  figure(rect[center]),
  figure(rect[right]),
)

#trans-linear(caption: none)
#trans-linear(caption: "Homegeneity")

image

This is much more manageable and easy to understand.