…am I really training aerobically during these first couple miles when I run them faster like this?
No.
So, am I fooling myself into bad behavior?
Yes.
By skipping a gradual warm up and instead immediately running just below AeT during these “warm up” miles, am I actually engaging my anaerobic engine (it kinda feels like I might be) and therefore depriving myself of the maximum aerobic base building I’m trying to do?
Yes.
Or is the body always training aerobically provided I keep my HR under AeT, even during these fast initial miles?
No.
Heart rate is bad proxy for exercise intensity.* There’s a lot of lag between executing the intensity and seeing its effect on heart rate.
The goal is to work at an intensity below your aerobic threshold. Your heart rate will only reflect that if your cardiovascular system is given enough time to adjust. And as fitness improves, it seems like the lag gets longer.
Something that will help a lot is to let go of the idea that you need to train right at your aerobic threshold. Just focus on staying below your aerobic threshold intensity. And a lot lower is fine: https://simplifaster.com/articles/how-trainable-is-vo2-max/
* Using heart rate to measure intensity is similar to Churchill’s comments on democracy: “It’s a bad system, but it’s better than all the rest.” (…because we can’t use power or pace in variable terrain.)