Is it obligatory to repeat the prayer for someone who used to recite the Tashahhud with "ashhadu anna" (أشهد أنَّ) with a shaddah on the noon, instead of "ashhadu alla" (أشهد ألَّا), knowing that he follows the madhhab of Ibn Taymiyyah, who does not deem it necessary to repeat the prayer for someone who unknowingly omitted an obligation?

The prayer is not invalidated by mispronunciation in the Tashahhud (definition). The correct way to recite it is to pronounce "an" with a sukoon (silent n) and assimilate it into the "lam." If you emphasize the "noon" and include the "haa," there is no harm, but the preferred and best approach is to use the wording found in the hadiths, with a light "noon" and its assimilation. You are not required to repeat past prayers, but rather to adhere to the prescribed method in the future.