The tax free allowance of £12,570 was frozen by the Tories with effect from April 2021.
Every time your State Pension is increased you will pay more tax on your works pension. Whatever your SP goes up by annually, multiple that by 20% and divide that by 12. That’s how much extra tax you will pay per month.
Assuming there is nothing else affecting you tax code, for example underpayments from previous years or other untaxed income, then …
Last year you paid £6 per month or £72 per year which meant taxable income of £360 (£360 x 20% = £72) so your income must have been £12,930 (£12,570 + £360 ). If your works pension is a fixed £528 per year, that means your SP was £12,402.
If you are now paying £15 pm tax or £180 per year that means taxable income of £900. (£900 x 20% = £180) This means your total income is £13,470. Deduct the works pension of £528, your State Pension must now be £12,942.
So it sounds like your SP has increased by £540. Impossible for me to reconcile that without knowing how your SP is made up.
This month, the main part of the SP was increased by 4.8% and Additional State Pension and Protected Payments, which aren't triple locked, by 3.8%.
Whichever it is, £540 x 20% is £108 - the extra £9 a month.
It isn’t HMRC’s fault. They just collect the money. The government sets tax policy and successive chancellors have retained the frozen tax personal allowance. It's tax by stealth but the same for everyone.