the meaning of "Come as many companies"
Solution 1:
JetBlue’s budget cuts(S) come(V) as(Conjunction) many airlines(S) continue(V) to struggle financially due to a significant decline in demand for air travel.
Its structure is "S1+V1 as S2+V2". S1+V1 is a main clause and 'as S2+V2' is a subordinate clause—an adverbial clause.
'as' has many meanings but the 'as' in your example means 'while' or 'during the time that' as Peter and user66974 said.
It is used to mean two actions occur at the same time like: She kissed about me as she hugged me.