Missing employment history

I have started my first work since end 2021, and have recently changed a new job after 3 years. I just realised on my HMRC app, my first employment history is missing, including tax payment and national insurance contribution. I have tried to report the missing employment history on the HMRC app, but instead received a self-assessment form to add 'current' employment. I have called HMRC for help and was advised to post my P60 and P45. However, I received another HMRC letter asking for more information to add 'current' employment. There is obviously miscommunication. Because of the missing employment history, HMRC assumes my new job was my first work, and so I think I am not paying the right tax for year 2024-2025.

Hi,
If you cannot update on your Personal Tax Account you may alternatively, contact HMRC to review/update here: 
 Income Tax: general enquiries.
Thank you.

I have contacted HMRC and was advised to contact my previous employer to resend my P60 and P45 forms to HMRC. However, my previous employer emphasized that they had reported my tax to HMRC and they did not find any error in their system. Please advise how I am able to proceed.