[sentence (plain form)] + という風に
[noun] + という風に
「Quote」+ という風に
The expression という風に (というふうに) is used to describe the manner or way in which something is done, thought, or said. It translates roughly to "in such a way that," "like," or "in the manner of." It is formed by combining the quotative という with かぜ風に (ふうに), which means "in the style/manner of."
という風に is used to specify how an action is performed, often referencing a particular way, method, or style.
It can describe someone's way of thinking or interpretation, expressing "in a way such that…" or "to the effect that…"
という風に is also used when summarizing a series of items or examples, similar to "like this" or "in this way." After listing several things, you can use this expression to wrap them up.
While このように is more formal and こんなふうにこんな風に is more casual, という風に specifically introduces the manner through a quotation or description – it tells you what kind of manner by spelling it out. This makes it useful when you want to explicitly state the content of the manner.