Is it obligatory to repeat only the Dhuhr and Asr prayers, or the rest of the day's prayers, after making a mistake in the Dhuhr prayer, forgetting the prostrations of forgetfulness, and then combining it with the Asr prayer out of necessity, especially since this happened some time ago?

You did not explain the nature of the oversight that occurred to you. If the oversight was of a type for which prostration is not prescribed, then the prayer is valid. Similarly, if it was of a type for which prostration is prescribed, such as omitting an emphasized Sunnah (definition), then the prayer is not invalidated by inadvertently failing to prostrate for it. However, if what was omitted was a pillar of the prayer, then the prayer is invalid due to the inability to rectify it, and only the invalid Dhuhr prayer and the Asr prayer that was combined with it must be made up. This is because if the invalidity of the first prayer becomes apparent after combining, then the combining becomes void, and both prayers must be repeated in their proper order.