Not sure if I am paying national insurance contributions or gap in records

I can't tell, whether or not people on contributory based Employment and support allowance get national insurance credits. I always thought I was stupid with paperwork but was diagnosed with Asperger’s in 2020, not that this is an excuse, I also think I have symptoms of ADHD but was told by my CPN that there is a 4yr wait list. I have read the info on here and the gov website and am still confused. I am worried I won’t get state pension, or I will have gaps in my record. I tried phoning 0300 200 3500 to ask if, as a recipient of contributions based employment and support allowance, am I paying NI stamps, but was on hold ages, and this stresses me out. I get 611.72 a month net works pension I am 56 years of age, and was “contracted out” (whatever that means) My pension is based on civil service where I worked from 1987 - 2003 when I went on sick and was retired in 2006 I get £7340.59 Gross pension a year I get 183.28 contributions based ESA every two weeks, (deductions made as I receive a works pension) I was incapacity benefit, from 2004, until 2014 I was medically retired in 2006 I just want to know if I have been paying into my state pension from my contributions based ESA, or, formerly incapacity benefit? Thank you.

Hi
Employment and Support Allowance (ESA) is paid by DWP and usually attracts Class 1 NI credits.  
A year covered by 52 Class 1 NI credits will usually be a ‘qualifying year’ which means that it will count towards pension entitlement.  
However as the credits are awarded by the DWP, who also calculate pension entitlement, they would be able to give a definitive answer to this question.
I am sorry you were not able to speak to an advisor when you called us on 0300 200 3500.
This is the NI helpline, it is usually quieter between 8am and 9am. Someone on this line would be able to look at your record and check if Class 1 NI Credits had been awarded, however if they have not been awarded, HMRC would be unable to say why, this would be a matter for DWP.
You can check your current pension position by opening a personal tax account (Personal tax account: sign in or set up) or by calling the Future Pension Centre (part of the DWP) on 0800 731 0175.
Thankyou.
Regards.