On the new History beta site I have the privilege to approve tag edits already but my own edits still go into the review queue. And the review dashboard displays a different number of pending edits depending on where I am: on https://history.stackexchange.com/review/first-answers I see one pending edit, on https://history.stackexchange.com/review/suggested-edits I see none. I am pretty sure that the pending edit being displayed is my own - I edited a tag wiki and that edit hasn't been approved yet. It shouldn't be counted no matter where I am.
Yep, you could call this a bug, that's certainly valid. However, this value is displayed on every page load and cached for the system overall.
It's a classic trade-off case between accuracy and performance, and in this case we're okay with 99% accuracy vs a severe degradation and complication on the performance side. I wouldn't expect this to change any time soon, it'll stay this way for performance reasons.