I found the following etymology of the word "ambassador" on Wiktionary.
From Middle English ambassadore, from Anglo-Norman ambassadeur, ambassateur, from Old Italian ambassatore, ambassadore, from Old Occitan ambaisador (“ambassador”), derivative of ambaissa (“service, mission, errand”), from Medieval Latin ambasiator, from Gothic 𐌰𐌽𐌳𐌱𐌰𐌷𐍄𐌹 (andbahti, “service, function”), from Proto-Germanic *ambahtiją (“service, office”), derivative of Proto-Germanic *ambahtaz (“servant”), from Gaulish ambaxtos ("servant"; also the source of Latin ambactus (“vassal, servant, dependent”)), from Proto-Celtic *ambaxtos (“servant”), from Proto-Indo-European *h₂m̥bʰi-h₂eǵ- (“drive around”), from *h₂m̥bʰi- (“around”) + *h₂eǵ- (“to drive”).
I'm wondering how Gothic 𐌰𐌽𐌳𐌱𐌰𐌷𐍄𐌹 (andbahti) became Medieval Latin ambasiator phonetically, especially how h in andbahti became s in ambasiator. I have read some books but still couldn't find a specific reason for this sound change.
Here is my personal explanation of this sound change:
This is a sound change of partial assimilation. h changed into s retaining its own fricative feature and gaining the alveolar feature from t. Then epenthetic vowels (between s and t) were added.
Still, I am not sure if my the explanation is correct. If yes, are there any other sound changes similar to this one?
Yet, I am also not sure whether h actually changed into s historically.
Edit: Thanks for the answers below, really appreciate them!