So, I've been very excited about my 2 year anniversary with the site, since it means a new pet! But Subeta doesn't seem to recognize that it's passed? Even though my profile says it's been two years and two weeks, the achievement is still only counting one year, and I haven't received my box. Am I just an idiot, and there's a certain page I have to visit like with some other achievements, or is this a bug?

You have to go to your User Dashboard. You should also get a 1 Week GA Medal because they added a prize for the first year achievement in the time since you would have hit 2 years. If you've been there and haven't gotten the box, then it's a bug c: