"Welcome to the NHK" (NHK ni Youkoso!) is an anime that is often praised for depicting social anxiety in a realistic and sensitive manner. It is based on the novel by Tatsuhiko Takimoto and follows the life of a socially withdrawn young man named Satou Tatsuhiro, who suffers from severe social anxiety and struggles to connect with others.
The anime delves into the challenges of living with social anxiety, the difficulties of forming relationships, and the mental and emotional toll it takes on the protagonist. It also addresses themes of isolation, depression, and the complexities of overcoming these issues. Many viewers and reviewers have appreciated its accurate portrayal of social anxiety and mental health struggles, making it stand out as a realistic depiction in the anime medium.
Keep in mind that there may be other anime released after i lost interest in that topic that could also depict social anxiety in a realistic way, so I recommend checking more recent sources for updated information on this topic.