Even though I don't know why bank statements don't include account number and IFSC code, I know that Axis provides details of individual NEFT transfers including account number and IFSC code and other details.
I'd probably send the other perwon who needs a proof, a video of me logging into my Axis mobile app, going through the process of seeing the history of the transaction.
We can download each such transaction detail.
Not sure how much it could help.
Similarly, whenever I send money by account number and IFSC code via Axis UPI (within the app), it retains the history that includes account number and IFSC code, just like NEFT with downloadable receipt in image form.
This is the closest thing I found.
It still doesn't answer the original post.