Here are two future events to be announced in writing:
A well-known poet, who is also a talented painter, is coming to the party.
A well-known poet and a talented painter (different persons) are coming to the party.
At first, it seemed to me easy to announce both the events— just using the verb form accordingly to the one subject in the first announcement and the two subjects in the second:
A well-known poet and (also) a talented painter is coming to the party.
A well-known poet and a talented painter are coming to the party.
But something seems to be wrong with the first one since the grammar checker keeps marking "is" before "coming" as an error, suggesting to use "are" instead.
Is there really some sort of grammar flaw in the first announcement?
If there is, what will be the right way to announce the first event sticking, if possible, to the model of the second announcement?