The syntax for embedded images in MediaWiki currently supports quite a few attributes, including CSS class, such as [[File:Example.png|class=...]].
However, it doesn't support CSS inline styles, like [[File:Example.png|style=...]].
We support inline styles for tables, and for divs and spans; as a user I would expect to be able to define styles wherever I can define a class.
In general we're very reticent to add more syntax to wikitext at this point, especially to media transclusion which we're considering re-writing from scratch (see T90914: Provide semantic wiki-configurable styles for media display). In particular, inline styles are almost certainly not going to happen (see this RfC on scrapping them, and T89134: Removing inline CSS/JS from MediaWiki for the bigger picture). Consequently I am declining this task.