the answer will vary widely depending on the type of insurance and the geographic location. In general you won't find out how much an insurance company will pay you until you get on the panel which is part of the problem and one of the reasons why many people choose not to take insurance. however it is a myth that people cannot make money by taking insurance, or that you cannot do psychotherapy. it's really a choice of how much you want to make, how much of a hassle it is to deal with billing at the like. but in the overwhelming majority of places in this country patients expect to be able to use their insurance to see a psychiatrist which makes it difficult to go out of network unless you are in specific areas.
also if you google some insurance companies will put the lists of what they pay for a given CPT code in that area but this is uncommon. Here is an example from the fee schedule from some years ago (so it would probably be higher now) for
Blue Cross Oregon. Note that oregon is probably the best in the country for psychiatrist insurance reimbursement so it could be considerably lower in a different state.