Is it obligatory to await the cessation of istiḥāḍah (non-menstrual vaginal bleeding) to pray in a state of purity, given that the time of its cessation is unknown or not always sufficient? And is it obligatory to repeat the prayer if the bleeding is later found to have stopped, or to delay the ‘Ishā’ prayer until the end of its time?

The most authoritative opinion is that if a woman's period of blood cessation is unknown—meaning it sometimes stops and sometimes doesn't, and the duration of its cessation sometimes lengthens and sometimes shortens, and it sometimes occurs earlier and sometimes later—then she should perform what a woman with istihada (prolonged non-menstrual bleeding) does: perform ablution immediately after the time for prayer begins, and pray her obligatory prayer and as many supererogatory prayers as she wishes. She does not need to repeat the prayer if the blood then stops, because she has done what was required of her.

Therefore, if you know that the blood ceases for a specific duration sufficient for performing purification and prayer, then you must wait to pray during that time, even if it is at the very end of the prayer's prescribed period. However, if the situation is as you described, where the blood may stop or may not, and its cessation period may be long or short, then perform ablution whenever you wish after the prayer time begins, pray, and do not repeat the prayer after you have finished it.