I do think that all you need to do is tell HMRC that your partner provided for you. I have known a few women in this situation. They usually simply need confirmation.
However, I wonder why they are asking now, and if there are other concerns. CAB & turn2us are 2 organisations that often help.
I would definitely investigate you state pension entitlement. You say that you are 65 and have not earned anything for 30 years. If you were earning before that, then in normal circumstances you would have either paid NI or been credited with contributions for possibly 17 years. You would then have had Home Responsibilities credit - and the exact ways in which this was credited has varied over the years, so definitely worth looking at. It is quite possible that you have a good number of years . The gov.uk website will tell you how to check that.
You may then consider buying extra years by paying a lump sum - again the exact details vary so you need to check out exactly how it applies to you.
For instance:
If you paid or were credited with NI contributions for 17 years (age 18-35) then had Home Responsibility credits for say 13 years, that gives you 30 years contributions, and you may well be able to buy a 'top up' to give you enough qualifying years. I know several people who have done that.
I know it doesn't apply to you, but in case others are reading: if anyone decides not to work because they are supported by another person, they can still pay voluntary contributions in order to claim their State Pension. I know a number of women who did that.