Thank you, friends! ‘Are’ is the correct option.
Verbs like ‘seem’ take adjective phrases as complement, but not participial clauses. They can therefore substitute for ‘be’ in (2), but not in (1):
(1) They are entertaining the prime minister and her husband. ✓
They seem entertaining the prime minister and her husband. ✗
(2) The show was/seemed entertaining. ✓
@GrammarT
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