Does the に work in the same way as in 残念に思う? Namely, the に marks the content of one’s thoughts?
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In a broad sense, yes, it belongs to what's described in your link. But in this specific case, ～くらいに + [mental/sensory verb] is more like a set phrase that can be replaced by ～ような（もの／こと）だと. It implies that the previously said content is an approximation or likening, rather than a faithfully manifested impression.