Anabeme

Hello, I recently looked at my HMRC profile via Government Gateway and was shocked to see that HMRC shows that I have been unemployed since I arrived in the UK (mid 2021) and have made no contributions to NI. There is nothing in the system at all. I didn’t make enough money to do self-assessment either. However, I was on the PAYE system and have all my payslips, P-60s, and my P-45. Rang up HMRC yesterday to see what my options are and they said to send my P-60s and payslips and they’d look into it. I sent it from overseas (currently on a small break between jobs). Is there anything else I should be doing? How long should it take to see updated in my HMRC account? Should I be also chasing payroll, too? Thank you.