If someone performed tayammum out of forgetfulness, then during the prayer remembered that they had been in a state of wudu previously, was it obligatory for them to exit the prayer and perform wudu again?

You are not required to exit the prayer if you remember that you were in a state of ablution (wudu'). Rather, you should continue your prayer because your initial ablution is valid and is only nullified by the known nullifiers of wudu'. As for someone who performed tayammum (dry ablution) and then found water during the prayer, they do not interrupt their prayer, even if they had hoped to find water at the time of tayammum, according to the relied-upon opinion among the Malikis. It is forbidden for them to interrupt it.