Sheikh Ul Islam Ibn Taimiyyah (May Allāh have mercy on him) said, “There is no doubt that some of the companions used to say “Bismillāhi Al Raḥmāni Al Raḥīm” (In the Name of Allāh, The Merciful, The One Who Bestows Mercy) aloud in prayer, and that some did not, but said it quietly to themselves or did not read it. Those who used to say it aloud would do so sometimes, and at other times would do it quietly. That is because it is largely Sunnah (the practice of the Prophet (May Allāh praise him and Peace be upon him) to do dhikr (remembrance) quietly, and one does it aloud for a greater benefit such as:

To teach those praying behind them: It is established in an authentic ḥadīth (narration) that Ibn ‘Abbās recited Sūrat Al Fātiḥah aloud in the janāzah (funeral prayer) to teach them that it is something from the Sunnah “[Majmū’ Al Fatāwā 22/274].

Sheikh Al Albānī (may Allāh have mercy on him) said, “The truth is that there is no clear authentic ḥadīth (narration) about saying “Bismillāhi Al Raḥmāni Al Raḥīm” aloud, but it was authentically related that the Prophet (May Allāh praise him and Peace be upon him) did it quietly to himself in the ḥadīth of Anas. This is the position of the majority of the majority of scholars of jurisprudence and most specialists in ḥadīth” [Tamām Al Minnah p.169].