Is it obligatory for one to interrupt a wet dream by waking up quickly if they feel it, or is there no blame upon them if semen is discharged during the onset of wakefulness?

The pen is lifted from the sleeper until he wakes up, and what you see in your sleep, you are not held accountable for.

If you wake up and are able to stop the thought that leads to ejaculation and not dwell on it, that is preferable.

Whoever intentionally ejaculates through thought without any physical action is not sinful, for Allah has forgiven this Ummah for what they contemplate within themselves, as long as they do not act upon it or speak it.

Masturbation by hand or similar means is forbidden. However, if one thinks and then ejaculates, there is no sin upon him, except that he should not think of a specific woman lest Satan tempt him. But if he thinks about the act in general, such as imagining intercourse with a woman, and semen is discharged, there is no harm in it, though it is better not to engage in such thoughts.

Ghusl (ritual bath) is obligatory upon the emission of semen in all cases.