The way you are currenly formatting it, I seperated the narration from MC's thoughts completely since there's "I thought" at the end of the internal monologue with the AI.
If there are 2 types of thoughts, one expressed through narration and one expressed through dialogue then I don't think there's a more intuitive way to it. I suppose a "I nearly jump as the AI responds to my thoughts." in the first interaction along with subtle reminders like "I'm still not used to the whole mind speaking thing." is ok enough.
Another thing about the formating, you could bold/italic all dialogues between MC and AI instead of quotation marks and ofc, show MC as the speaker to make it clearer, but that's just imo.