How did Gothic "𐌰𐌽𐌳𐌱𐌰𐌷𐍄𐌹" (andbahti) become Medieval Latin "ambasiator"?

Question

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!

Answer 1

I think a likly path to the "s" is through "kt" (as in ambactus) which then palatalized before j. A variety of spellings are apparently found in this word and related words such as ambascia: single s, double ss, x, sc, c.

It's a bit hard for me to find similar examples of the outcome of Latin -cti- in Romance languages, but perhaps the -ss- in French cuisson, which is supposed to be from Latin coctio, is analogous.

The t in -ator is originally part of the Latin agent noun ending, not part of the stem found in 𐌰𐌽𐌳𐌱𐌰𐌷𐍄𐌹/ambaxtos.

Answer 2

The shift of /k/ to /h/ is regular in Germanic (assuming that the borrowing from Celtic to Germanic is very old: i.e. pre-Grimm). But I do not see why the Romance forms should derive from Gothic, rather than directly from Celtic. The development of -kt- to Italian -sc- and then to French -ss- does not seem problematic.