Is it obligatory to repeat the Asr prayer after adding a third prostration to it due to obsessive thoughts, knowing that the addition occurred after hesitation and recollection during prostration?

If you continued the third prostration after realizing it was the third, then you have intentionally added to the prayer, and therefore you must make up that prayer. However, if that was under the influence of waswas (whispers/obsessive thoughts) and you were unable to repel it, then you do not have to make up the prayer, because in essence, you were compelled. It is obligatory to resist waswas and turn away from it.