Check how the styles work in your html document.

My problem was that the styles were included via the <link /> tag, and Yandex-Metrica could not download these styles correctly.

When I inlined the styles into the <style>...</style> tags (yes, the html gained a bit of weight), but this helped display the styles in WebVisor.

Also, if you use webpack, check how you collect styles for dev and prod modes. If the MinExtractCssPlugin plugin is used for Prod mode, it forms all your styles into one file and includes them in the <link> tag. If this is the case, try not using this plugin and test the behavior.