Is the prayer valid if one doubts its type while sitting between the two prostrations, then remembers its type when moving to prostrate?

If one doubts during prayer whether they made an intention or not, or doubts whether they intended Zuhr or Asr:

If they remember before performing any action while in doubt, they build upon what has passed of their prayer, and their prayer is valid. However, if they perform an action while in doubt, their prayer is invalidated according to many scholars, though some scholars hold that it is not invalidated.

Shaykh al-Islam Ibn Taymiyyah holds that whoever doubts whether they made an intention or pronounced the takbirat al-ihram (opening takbir) should restart the prayer, because the default assumption is the absence of what is doubted.

If the worshipper remembers that they intended or pronounced the takbir before cutting off the prayer with their intention or starting any action within it, then they build upon what has passed, because no invalidating factor has occurred.

If they remember after having performed some action from it, Ibn Hamid holds that they still build upon it. However, al-Qadi holds that this invalidates the prayer.

Shaykh al-Islam also holds that if one doubts whether they entered into a supererogatory (nafl) or obligatory (fard) prayer, they should complete it as a supererogatory prayer, unless they remember that they intended the obligatory prayer before performing any action.

If one doubts whether they entered into the Zuhr or Asr prayer, is this the same as doubting the original intention or the intention for the obligatory prayer, according to the two views?

In summary, you should repeat the prayer if you doubt the specific intention and perform an action while in this doubt, such as beginning to move into prostration; this is because such an action invalidates the prayer according to many scholars.