What are the criteria by which something is considered an innovation (bid‘ah), and is it considered an innovation to invent a new supplication (du‘aa’) or to regularly recite a specific surah in a specific prayer—such as Surah Ad-Duha in the Duha prayer, or Surah Al-Fajr in the Fajr prayer?

What you mentioned about innovating a specific supplication and regularly reciting it at a particular time, or reciting a specific surah in a particular prayer, which the Shariah did not specify, it is feared that it falls under the category of an additive Bid'ah (innovation); because it is likening what is not sunnah to what is sunnah.