Thanks — this is a reasonable ask, and most of it is straightforward. Some notes on what I can do and one thing I have to be careful about.
The banner has sixteen separate colour controls today. A single master colour that fills all sixteen would be the wrong thing, though: set it to your brand blue and the button text goes blue on a blue background. So the useful version is not “one colour everywhere”, it is one colour for the parts that carry your brand — the primary button, the active toggles, the links, the revisit tab — with text and background colours derived rather than copied.
That derivation is something the plugin can already do. It ships a WCAG AA contrast checker that watches nine foreground/background pairs, so given your colour it can pick the text colour that stays readable on it instead of leaving you to test it. This matters more than it would on an ordinary widget: a consent banner has to be legible, and its Accept and Reject buttons have to carry equal visual weight, so a colour scheme that quietly fails contrast is a compliance problem and not only an aesthetic one.
So the shape I would build is a Theme colour field at the top of the Colours tab, which fills the brand-carrying controls and derives readable text colours. The existing sixteen controls stay exactly where they are as the advanced view, and anything you set by hand wins and is never overwritten. Nothing changes for existing sites unless the field is used.
On automatic detection — your “possibly overengineering” idea — it is actually the cheap part on modern themes. Block themes publish their palette through WordPress itself, so I can offer your theme’s own colours as suggestions next to the field. Classic themes publish nothing of the sort, so there it would stay a manual field. I would offer the palette rather than apply it silently: guessing a site’s brand colour and changing the banner on its own is not a surprise anyone wants.
One caveat on scope: this is admin-side convenience, so it is not urgent work in the way a broken banner is, and I will not promise a version number. I have logged it and it is a good candidate for the next feature release.
Thank you for your elaborate answer and all your points make sense. Glad you think of it as a considerable feature and understand this may take a while.