I would say, in the first instance "is" is the present tense of "to be", as you say. "relaxed" is a past participle used as an adjective (attribute)/cf: your body is beautiful. In the second instance, "restaurant" is absolutely NO adverb; it's a noun, the whole meaning "the staff of the restaurant".
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Can we say "the restaurants staff"? I mean in general.
So it's like in "a 3 day journey/ a 3 days' journey", the noun is used as an adjective?