I am not aware of any recent studies that directly link the consumption of red meat with prostate cancer recurrence. As far as I know, earlier studies that showed potential links between red meat consumption and prostate cancer recurrence have since proven to be unrepeatable.

Some studies link saturated fat with a higher risk of prostate cancer recurrence and mortality, potentially due to its impact on inflammation, insulin-like growth factor (IGF-1) levels, and lipid metabolism pathways within cancer cells. These studies have more recently focused on dairy milk products and poultry with skin, although the underlying mechanism would also apply to red meat (saturated fat).

You will find many sources of diet recommendations for prostate cancer patients that recommend limiting red meats and processed meats, with UCSF and PCF the most often cited sources:
https://www.pcf.org/patient-support/physical-mental-wellness/nutrition/
ttps://www.ucsfhealth.org/education/nutrition-and-prostate-cancer

The basis of the recommendations from UCSF and PCF is diets that reduce inflammation and improve the immune system, because both of those objectives are believed to improve the patient's ability to recover from treatments and the effectiveness of treatments. You will find reference studies on both the PCF and UCSF websites, along with contacts at both organizations who should be able to answer your questions about the prostate cancer diet.

I'm a curious patient and not an expert. There are others in this forum who are far better educated on prostate cancer diets and the basis of those diets, so I hope those people provide you with better answers.