Is it permissible for the husband to raise his voice during the entire prayer (even the Tashahhud) so that his wife can follow him and repeat the Pillars (Arkan) that she cannot perform due to her obsessive-compulsive disorder, and is her prayer with him considered sufficient?

Obsessive-compulsive disorder (OCD) is an illness with causes and treatments. However, the method mentioned in the question might exacerbate and solidify the disease, so it should be avoided. When reciting Al-Fatiha, if a 'waswasa' (whisper/insinuation) occurs that it wasn't recited or that something in it was omitted, one should not pay attention to these whispers, because the doubts of someone who frequently experiences doubts are inconsequential.