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The payroll system knows only what you earn from SAS, and what withholding information you tell it. It is possible that as you accumulate wealth over the years, you might also have a good bit of interest income, capital gains, a side hustle, a spouse who does not have enough withheld, and so on that drives up your taxes. At the same time, if you are itemizing deductions when you file, then the payroll system won't know about reducing your taxes.
Fortunately the circumventions are easy. If 6-10k is what you end up owing each year when you file, then update your W4 so that an extra $500-$800 is withheld each month. I do this each year to account for interest income and income from my spouse's side hustle.
Updating the W4 helps you pay your taxes, but does not help you lower them. To lower them (legally), try some strategies such as alternating years in which you make charitable contributions. One year give double, the next year give none. In the year that you double, doing so might put you over the standard deduction so that you can reduce your tax bill. In the year that you give none, then you can still take the standard deduction. In the end, you are still giving the same amount to charity. Using a donor-advised fund is a handy tool to facilitate such a strategy.
Here's a tip. Each summer, the AARP website updates its tax calculator so that it works for the next year. https://www.aarp.org/money/taxes/1040-tax-calculator/ So in say July, use that calculator to see whether your withholding is on track to approximate what you will owe in federal taxes. If you are off by more than what you want, then you can make an adjustment to your W4 in July so that you will be on track for year end. By July, you should have a good estimate of what your total income for the year is going to be. Run it again in August to see whether you need to adjust again.
Some combination of the above should help eliminate the tax bite.