You can ask to be contracted with the large volume insurances in your area and then they'll send you the rates, at which point you can try to negotiate (not all will).
You'll need to consider the factors that may lead to higher reimbursement rates when comparing with other practices, such as group practices which tend to have higher rates due to negotiating power, subspecialization (child, addiction, etc), and location (i.e., supply/demand). Not sure if time in practice, whether telehealth or in person, training prestige, or if you are part time/volunteer faculty at an academic institution matter.
There's a website where you can search Medicare rates in your area.
Scour PsychologyToday, Talkiatry, Zocdoc, Zencare, or any other psychiatrist directory and then go to their website to see if you can find their cash rates. Sometimes you have to download their patient agreement form to see it rather than being easily found on their website.