A bit late to reply, but hopefully someone will find this useful;
This is a legitimate extension which is shipped as part of Vivaldi. This functionality is included as part of a few browsers, though some use a different approach to get the same result. Because it is bundled as part of the browser, it does not show up in the list of user-installed extensions. This is the case for a couple of other extensions too, such as the one that displays PDFs in the browser. However, you can disable it using Vivaldi menu - Settings - Webpages - Picture-in-Picture Button on Videos. (The PDF viewer can be controlled in the same part of the settings.)
The extension is used to display picture-in-picture; it allows a video to be displayed on top of the browser while you are browsing other websites. It is configured to work with a specific set of popular websites that make this possible. When a page loads, the extension injects some scripts. The scripts then fetch the extension's configuration file locally from the extension. This loads not via the network, but by a local file read. Presumably, this is what you are seeing in the developer tools.
Basically, it is harmless and expected behaviour, and it is not something malicious.