What is the reason why に is used in this sentence instead of が or を?
Does this いただく here stand for honorific of する or of もらう?
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I think it's from もらう here. 〜に〜してもらう is used to express that you "receive the action from someone". They do it for you and に is the marker for the person doing it.
いただく makes it humble, so you express that it's something like a favor for you.
お集まり is the honorific version of 集まる. As you are using いただく afterwards, you don't need the する anymore. It seems almost like a nominalization to me.
The whole sentence sounds like "We have assembled people here who are working in a foreign language", literally "We humbly received (the favor of) assembling from people who are working in a foreign language".