I'm in a similar situation the OP.
I've lived overseas for some time and paid annual voluntary contributions, and I received a letter saying I'd paid enough to receive full pension, so i stopped paying NIC annually.
Then unknown to me they brought in the new state pension, and a year ago a friend tipped me off about the deadline for paying backdated NIC by 05 April 2025.
I got myself a HRMC website account which showed under the new pension system I would fall short of full pension but could pay a lot of money to backpay the more expensive (class 2?) NICs to catchup to get full pension.
I commenced writing to the Pensions dept in June 2024 and sent the necessary form to enquire how much to pay (as i wasn't convinced by the amounts the website said i had to pay, seemed too much) and after sending 3 letters (twice I sent the form) I finally received a letter late 2024 informing how much to pay for each year for the cheaper NICs (class 3?) as backdated payment to receive full pension. So I was right, the website says I have to pay the expensive class 2 but on checking was told I could pay the cheaper class 3.
In January 2025 I made a payment for the cheaper class 3 amount ( from mu Uk bank account to their bank account) for the outstanding years between 2006 and April 2025. There is an explanation online of the banking reference you have to create when making the payment so they know it's from you.
February 2025 having heard nothing I called. 30 minutes wait, put through to a lady in Glasgow. She confirmed she could see the amount I paid and the relevant people would be in touch soon.
Having heard nothing I filled a form in online in March 2025. Form says 10 days for reply. No reply.
End of March did the 'call back form' before 05 April deadline date, required to ensure catch-up payments before 2019 can be paid. No reply yet.
My HRMC online account for NIC shows the same as it has for the past year (that I have alot of unpaid years at the expensive class 2), but my Pension page online since 05 April now shows my estimate and forecast pension have increased alot compared to the amount before 05 April, so I'm hopeful I've almost sorted out my pension problem, but i can't be sure.
I will probably call them again in a week or 2 to check out the true situation with my NIC, my payment and my pension amount.
It's not easy is it!