Linux Vivaldi builds use libffmpeg.so from chromium-ffmpeg, which includes decoders for most codecs used on the web (no h265/mpeg2 tho), and VA-API which will handle all hardware accelerated codecs on particular platform.
This looks similar to using Microsoft provided Media Foundation codecs. No idea why Black Magic doesnt do it like Linux Chromium browsers.
Do you have any information on how the actual patent licensing is set up for Vivaldi? I wasn't able to find much on it, though I see the note in https://wiki.archlinux.org/title/Vivaldi that it “automatically downloads” the relevant files, which is at least suggestive that they can't just redistribute the binaries normally. The other closest thing I was able to find was https://github.com/chromiumembedded/cef/issues/3559 which describes a specific proprietary_codecs option in CEF, which is not quite the same thing but ought in some sense to be related… the way they describe having to set ffmpeg_brand=Chrome normally for that to be available doesn't sound promising?
I would be moderately surprised if whatever arrangement is going on there allows full use of the codecs for video editing software and not just for consumer decode of Web resources.