When searching inside a note, Obsidian puts a <span> element with class obsidian-search-match-highlight around the matched text. That allows to style the highlight.
However, for some reason, Obsidian does not put that <span> around matched text inside the properties when in live preview. Since the text is not marked, this cannot be remedied via css.
In Source mode, however, the span mechanism is applied to front matter too (even to property names), so you can temporarily switch to source mode to see it. I have mapped a hot key (Shift+Ctrl+E) to switch back and forth to source mode.
Oh, I see. In your case the values of the properties were wikilinks. Frontmatter Links plugin wraps them in a <a> tag, which removes the <span> used by Obsidian to mark the matching text. That explains why it is found nevertheless later in the main body, where the plugin did not interfere.