Note 9 at Ac 27:21: Why did Paul go on a long fast in this situation? Hadn't the Lord personally appeared to him and assured him that he would testify of Him in Rome (Ac 23:11)? Couldn't he just rest in the Lord and His promise?

It is possible that Paul was confident that the Lord would preserve him personally, but he was seeking protection for the others who were on the ship with him. When he did finally hear from the Lord, the Lord specifically mentioned that Paul had been granted the lives of the others (Ac 27:24), implying that this was part of his request.

It is also possible that even though Paul still believed God's promise, the circumstances were stealing his hope. That was certainly the case of the crew, and even Luke expressed hopelessness in Ac 27:20. "Faith is the substance of things hoped for" (Heb 11:1). Therefore, if Paul allowed his hope to crumble, his faith would follow suit. So this fast could also have been for him personally, to maintain his faith (see note 1 at Mt 4:2).