After a short delay of a few hours, Blizzard has now launched StarCraft Remastered.
Assuming you have the game purchased on your Blizzard account, The Blizzard App should now include StarCraft as a game on the left side of the app. It was missing earlier but it’s there now.
The download of the game is 5Gb which is tiny compared to today’s standards so it should not take long to download. Once you have it, enjoy the remastered visuals and audio. Hopefully it’s been worth the wait.