The good thing about being in NHS scheme is that there is loads of information about it on their websites, accessible to anyone.
www.nhsbsa.nhs.uk/sites/default/files/2019-08/Early%20Retirement%20factsheet%20%2805.2017%29%20V3.pdf
Yes, you can take an NHS pension at 55. You’re just young enough to still be under the 55 legislation, it will very likely change to 57 (or rather: State Retirement Age minus 10) in 2028.
However, for the portion of your pension (if any) in the 2008 scheme it will be reduced by 40%, and by 45% for the 2015 scheme portion.
So basically you’d have to be desperate to do that! Even without £300K sat in a DC scheme.
However, it’s not as simple as just taking 25% from your £300K. Once you go into drawdown on any pension, subject to a few small exceptions, you trigger the MPAA which limits your future DC contributions - potentially blocking you off from some significant tax relief. It doesn’t impact the DB contributions so if you remain an NHS nurse it won’t impact those contributions. It’s not something you have to think about today - but it’s why you need to get a good understanding before making final decisions. You can take 25% of that £300K tax free without triggering the MPAA - but only if you don’t take anything more from it. Once you do - annual contributions limit is triggered.
Why do you need to top up your income from 57-67? You can already save £300 a month and presumably at 57 though you’ll receive no maintenance, you also won’t have young dependent children.
Interest rates are at an all time low. If that continues, I’d just carry on paying mortgage as usual until you’re 65. Your £300K pension savings will likely increase at a higher rate than your mortgage interest.
Whether you overpay or pay into pension now is based partly on numbers and partly on personal comfort with risk levels and just preference - it can be a big deal to feel a mortgage is paid off. But purely on numbers, it’s unlikely to be worth overpaying the mortgage, if interest rates stay low.
Do your research on how your £300K fund is performing. You’re in a good position with that.
Check your state pension and make sure you have all possible qualifying years so far, and budget for buying extra if needed. That is laughably cheap for what you get - so I’d personally buy sooner not later in case it’s withdrawn.