What is the ruling on my continuing to pursue a Ph.D. at the university, knowing that I completed my bachelor’s degree through the external affiliation system, which violates the admission and registration requirements, and I did not mention this when submitting my documents?

The admitting authority is supposed to scrutinize the documents. If it knew that you studied under the affiliation system and overlooked the condition, then there is no sin upon you in continuing your studies. However, it would have been better if you had inquired about the matter to guard against any potential error.