There are two kinds of empathy humans experience: Cognitive Empathy and Emotional Empathy. These are unrelated to interoception (or alexithymia), or the ability to recognize your own feelings and emotional control.
You can be very empathetic and still have trouble controlling your emotions. I’m autistic and work with adults on the spectrum, and while it for sure is a spectrum, most of us struggle with cognitive empathy but are highly sensitive with emotional empathy.
Dziobek et al. (2008) utilized the “Multifaceted Empathy Test” to prove that autistic adults showed deficits in cognitive empathy but no deficit in emotional empathy compared to controls.
Mazza et al. (2014) replicated these findings in adolescents, showing that autistic participants had difficulty interpreting mental states (cognitive) but were fully capable of empathizing with the emotional experiences of others (affective).
Bird and Cook (2013) argue that the emotional symptoms often attributed to autism (like dysregulation) are actually due to co-occurring alexithymia.
Mul et al. (2018) found that alexithymia mediates the relationship between interoception and empathy, supporting your claim that these are distinct but interacting mechanisms.
You can be highly intelligent and have high Emotional Empathy (feeling everything) but low Interoception (not knowing what you’re feeling), leading to a meltdown rather than ‘Emotional Intelligence.’