I assume it would just be downloaded into your hidden config folder of the specific browser in your home directory. At least that’s the way Firefox handled it. No notification for package management. Firefox used to ask,if the widevine plugin should be downloaded. Don’t know, how it is handled today. Didn’t use/need widevine for quite some time.
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firefox also use widevine, but it downloads if you enable it… was searching in chromium like it does in firefox but see no option, sure chrome://components you enable that offcourse 
atleast firefox is not so vague…
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Yes & no. If you check the contents of /opt/vivaldi/ there should be two shell scripts. One for installing/updating widevine (update-widevine) & one for installing/updating ffmpeg (update-ffmpeg). You can use pacman transaction hooks to invoke them post installation/upgrade, like this:
Hence, the installers are bundled, but I don’t know whether the actual extensions can be.
Clearly, the existence of this thread indicates otherwise. 
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chrome://components wil also do
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