Is John 8:7 an example of Jesus serving as a social worker?
The answer to this depends to some degree on what you think the status of this woman is and why she was about to be stoned.
Social workers are people who help others to deal with problems in their lives. However, we typically say that they help people to deal with problems that are brought about by issues that are in some way beyond their control. For example, if people are disadvantaged by poverty or lack of education, social workers can help them. If they are disabled physically or mentally, social workers can help them. On the other hand, we would not typically say a social worker would be working with someone who simply chooses to act badly. Therefore, the exact status of the woman is important.
The story in John does not tell us anything about her other than that she was caught in adultery. If this happened simply because she had fallen in love with a married man, or with a man who was not her husband, Jesus is not really acting as a social worker in this verse. However, if she was actually a prostitute because she had no other way to support herself, he would be acting as a social worker. If she had been beaten by her husband and had turned to adultery because of his actions, he would be acting as a social worker. This would be particularly true if he were to in some way follow up with her in the same way that he followed up with Mary Magdalene after the demons were cast out of her (we could see that as a mental illness).
So, whether Jesus is a social worker here depends in large part on the exact causes of the woman’s trouble.