Is the prayer of one who suffers from incontinence and was compelled by obsessive-compulsive disorder to delay the Dhuhr prayer until the time for Asr began, then completed Dhuhr, then performed ablution and repeated Dhuhr and prayed Asr, considered valid?

If your (ritual) impurity is continuous and your ablution becomes invalid upon the expiry of the time (of prayer), then if the time expires while you are praying, you should cut off your prayer, perform ablution, and repeat the prayer. The Shafi'is hold that the ritual purity of a person with an excuse (ma'dhur) does not become invalid upon the expiry of the time if they delayed the prayer, and the Malikis agree with them that the purity of a person with an excuse does not become invalid upon the expiry of the time. In your situation, we advise you to act according to the Maliki school of thought, as it offers ease. So, continue with your prayer even if the time expires, and do not repeat ablution afterward; rather, pray the second prayer. You should not repeat the prayer after completing it so that obsessive thoughts (waswās) do not persist.