Is your feature request related to a problem? Please describe.
Currently, new buttons or buttons loaded without a set color will default to a gray where on the web they use a color set by the theme from the css class .wp-block-file__button.

We now have support for theme colors in #2241 and we'd like to adjust the gray to be a color loaded from the theme.

Describe the solution you'd like
Ideas that were proposed in WordPress/gutenberg#22197 (comment) were to use the first color from the color palette, but provide a warning that this might not be the correct color.