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Both a lot of information, and not a lot of information travels through those cables.
It’s going to depend a lot on where you live.
If you’re in North America, the vast majority of the services and websites you access will be hosted on the continent and will continue working just fine. Webpages for European companies may become inaccessible.
If you’re in Australia, some local stuff will continue working, but a lot more things will die.
Services like Netflix almost always have local servers, it’s not financially reasonable to push that much video between continents on a per user basis. They just use those links to sync their various servers as new content is released.
Most phone calls to foreign countries will fail. Almost all of it passes through the internet cables these days, rather than using dedicated phone lines undersea.
“it’s simply not my problem”
Yes it is