When placing formatted text in Affinity Publisher from a Word document that didn't use Character Styles for italics and bold, I've found that applying a style and preserving local formatting won't update the paragraph indent, among other things. If one wants such properties to also be updated without losing italics and bold formatting, one can reapply the style and preserve character formatting.
In my case, my text originates in Scrivener. I compile to create a Word document, which I use in Kindle Create to create my e-book. For the print book, I place the Word document in an Affinity Publisher document. In Scrivener, I've never messed with Character Styles, and have never investigated whether that's something Scrivener even supports. After I place the text from the compiled Word document into Affinity Publisher, I update the paragraph style with a three-step process: 1) Select consecutive paragraphs that need the new style applied, 2) apply the new style, preserving local formatting, 3) apply the new style again, preserving character formatting. The order here matters. I end up with updated paragraphs that have the desired style but with my original italics and bold passages preserved.