I tend to find good examples of data-driven blog posts on Gov.UK; GDS has done a lot to drive better decision-making with strong data. An example of that is the Input component they use [1] and the data behind the choice and issues with type=number [2].
On the making more money perspective, I can share an anecdote for you, when I was working with a large property portal in the UK, we had a few unstyled dropdowns hanging around the app for sort criteria etc. Simply replacing them with a styled dropdown (and dropdown list) resulted in a 60% uplift of using that sort. We made no functional changes, just styled it. And it wasn't good styling, we broke dropdowns (as many do) in the first iteration (we were testing the hypothesis that people didn't use it because it didn't look like it was our component / wasn't styled like the rest of the site) -- So yes, anecdotally, pretty can be more impactful and result in more clicks.
EDIT: Missed the appendice links
[1] - https://design-system.service.gov.uk/components/text-input/
[2] - https://technology.blog.gov.uk/2020/02/24/why-the-gov-uk-des...