You can file an appeal against a denial. Your therapist will help you with this.
Privately insured people should clarify reimbursement individually with their insurer. For inpatient treatment, separate rules apply, which depend on the insurer and the payer. Costs for self-pay patients are based on the fee schedule.
My own service lies outside the statutory health insurance system. This service is psychological counseling, not psychotherapy. It is not intended to diagnose, cure, or alleviate illnesses. You pay for the online counseling in German via video yourself, without an application or an expert reviewer. In doing so, I look at relationship patterns and early formative experiences from a depth psychology perspective.