Вы можете сделать:
void checkString(std::string x,std::regex e){
std::smatch m;
while (regex_search(x, m, e))
{
std::cout << m.str() << '\n';
x = m.suffix();
}
}
int main(){
std::regex e(R"((?:https|http):\/\/media\.discordapp\.net\/.*?\.(?:png|gif|jpeg|jpg))");
std::string example="dadasdasdhttps://media.discordapp.net/Js1VPuxC5xs.pngdsdhttps://media.discordapp.net/Js1VPuxC5xs.gifsdhttps://media.discordapp.net/Js1VPuxC5xs.jpegsddshttps://media.discordapp.net/Js1VPuxC5xs.jpg";
checkString(example,e);
}
Демо