About waking at 6:00 AM
Six is the most-set alarm time there is. It gives a comfortable margin before a nine o'clock start, and it lands close to the natural cortisol rise for a lot of people, which is why waking at six often feels easier than the clock alone would suggest.
Leave the tab open
A browser alarm can only ring while its page is open. It does not have to be the tab you are looking at, and on a desktop it does not have to be the window in front — but closing the tab or quitting the browser stops it. For anything you genuinely cannot miss, set a second alarm on your phone as a backup. That is true of every browser-based alarm clock, not just this one.