Continue VET TEC Authorization Act of 2023 This bill requires the Department of Veterans Affairs (VA) to implement through FY2028 a program similar to the Veteran Employment Through Technology Education Courses (VET TEC) pilot program (which this bill terminates at the end of FY2023) under which the VA provides up to 6,000 covered individuals per year the opportunity to enroll in high technology programs of education that provide non-degree training or skills related to computer programming, media application, data processing, or information sciences. A covered individual is a veteran who (1) is under the age of 62, served an aggregate of at least 36 months on active duty, and was discharged or released from service under conditions other than dishonorable; or (2) will satisfy such requirements in fewer than 180 days after the VA's determination. In administering the program, the VA must provide assistance to covered individuals in amounts equal to those provided to Post-9/11 GI Bill recipients who are pursuing a degree on more than a half-time basis. The VA must seek to enter into contracts with any number of qualified providers of high technology programs of education and pay such providers a specified percentage of the tuition and other fees for each enrolled individual. The bill prescribes (1) requirements for a provider of a program to be considered as qualified (e.g., the provider employs instructors the VA determines are experts in their respective fields), and (2) criteria for the VA to approve providers for contracts. If a covered individual has remaining entitlement to other VA educational assistance, entitlement under this program must be charged at the rate of one month of that remaining entitlement for each month of assistance under this program.