Do I need life insurance if my pension pot is big enough?

Embarrassingly, I only discovered today that on death, my pension pot is giving to my family/estate in some capacity.

Doesnt go to your estate. It goes to a beneficiary outside of the estate. If you have given no nomination/expression of wish then the trustees will be left to decide who gets it.

Assuming my pension pot reaches a similar level to my life insurance pay out (£150k in this case), is there any real need for the life insurance?

£150k of life assurance is not much nowadays. However, we dont know what your financial needs are. Is your pension fund worth £150k now or later? Maybe if it hits it later and just £150k is all your need, then maybe you dont need it.

Am I missing some subtlety of how the pension pay-out would work, or misunderstanding anything?

No. Advisers usually include pension payouts in their shortfall analysis. So, all quite normal.

However, you may be understating your financial need if you are looking to cover the mortgage, other debts, kids, loss of income, reduced pension benefits etc. You should carry out a shortfall analysis before you do anything else.