Does hesitation about interrupting an ongoing prayer, or thinking about doing so, necessitate interrupting or withdrawing from it? And is it considered a mistake to say "Allahu Akbar" aloud in a voice that can be heard by the person next to me?

The treatment for obsessive thoughts (waswas) is to disregard and ignore them. No matter how much Satan whispers to you to interrupt your prayer, do not pay attention to his whispers. Rather, the worshipper should continue their prayer without hesitation in starting it. Begin the prayer immediately, without caring about the obsessive thoughts. And beware of interrupting your prayer in response to them. Do not raise your voice with the takbir (Allahu Akbar) so as not to disturb those next to you; instead, move your tongue and lips such that you can hear yourself. The prayer is not invalidated by raising the voice, but one should strive against oneself to abandon this practice so that other worshippers are not bothered.