Does lowering the hands after the intention for prayer and before the takbir constitute a break in the intention, necessitating its renewal, or is the initial intention sufficient as long as the attempt continues? And is it obligatory to say the full phrase "I intend to pray the fard of Isha", or is "the fard of Isha" sufficient?

The cure for obsessive thoughts (waswas) is to ignore them and pay them no mind. The matter of intention (niyyah (definition)) is straightforward: it suffices to bring to mind the prayer one intends to perform. One must initiate the takbir (Allahu Akbar) promptly, without hesitation or lingering with obsessive thoughts. If the takbir is delayed by a short time after the intention, the intention is not invalidated, as it is permissible to precede the act of worship with the intention by a short time. Indeed, some scholars have permitted preceding it by a long time, as long as the intention is not broken. One must strive against oneself to repel these obsessive thoughts and not give them any attention.