This is difficult to prove. The author of the original claim, Corinna Santa Ana, posted through LinkedIn, making it very easy to check their work history. She has been working as a freelance writer for 8 years, and most of her work before being a freelance writer does not involve healthcare with the exception of her work with the Diabetes Hands Foundation. When googling her name, she primarily shows up as a diabetes advocate and writer, but I could find no claims that she was disreputable.
The claim listed her does not seem to appear in her article. When reading through it, she did not claim that Oprah was taking Ozempic, but rather that she had discussed it. The article she linked from People Magazine also does not claim that she was taking the drug. People Magazine, according to Media Bias / Fact Check is considered to be a reputable source. It is worth noting that the linked article is from November of 2023 and that the article from People is from September of 2023.
In December of 2023, People Magazine did an exclusive interview with Oprah where she admitted that she had begun using weight loss drugs in combination with exercise and other holistic health practices to aid her weight loss journey. This report came out after the Santa Ana article, and anything claiming that Oprah was using Ozempic before this report can be considered speculation. However, it is also important to note that the December article does not name the weight loss drug(s) Oprah has been using. Her interview says that she was prescribed drugs through her doctor for weight loss, which the original Santa Ana article implies is not how Ozempic is acquired; at her time of writing, "the FDA [had] approved Ozempic for use by people with type 2 diabetes to reduce glucose levels, but not for use as a weight loss agent." This claim, cited directly from the FDA, makes it seem unlikely that Oprah is taking Ozempic specifically, despite the truth to her using weight loss drugs.
Ultimately, the specifics are difficult to prove, but part of the claim has been proven to be true.