Not all income is taxed at the rates you cite. Special rates apply to long term capital gain and qualified dividends (maximum rate 20%). There are $1,349 of qualified dividends in this case and $3000 of capital losses that can be taken in the current year (this is the cap for capital losses against ordinary income).
The benefit the Warren receives from these special tax rates is negligible.
There are also above the line deductions ($59,348) and itemized deductions (they claimed $60,128 of them that reduce their taxable income), credits (which reduce taxes dollar for dollar of which they claimed $13,936) and the carry forward of losses that couldn't be claimed in full in a prior year for some reason (which is functionally similar to a deduction) of which the Warrens have $102,276 but could only use $3,000 in the current year.
While they doesn't appear to be included in the $905,742 of gross income figure cited, certain kinds of income are also exempt from inclusion on a tax return such as qualified municipal bond interest, certain income in the form of wages and salaries earned abroad, certain disability payments, personal injury settlements (exclusive of interest components) and alimony received under a post-2017 divorce decree, to name a few. None of these items are relevant for Warren.
According to @JackFleeting in his answer:
they had gross income of $905,742, AGI of $846,394, taxable income of
$786,266 and tax liability of $230,965
Per the chart, the tax due on ordinary income of $786,266 is $229,058 by my calculation. This is reduced by a $13,936 residential energy credit (because she installed solar panels on her home), and $8,696 of additional federal tax as self-employment taxation, and $6,137 of self-employment and Obamacare taxes netted against overwitholding of Medicare taxes.
The itemized deductions were $60,128 which consists of state and local income tax payments (limited to $10,000 of $78,086 incurred in 2018) and charitable deductions of $50,128 (about 5.5% of her income).
Warren herself, like most middle and upper middle class people in the Northeast, fares very badly with respect to deductions in 2018 compared to all prior years when they were not subject to a $10,000 cap.
For reference purposes, the disallowed itemized deductions increased her tax bill by $25,192 (itemized deductions don't impact the amount of FICA, self-employment tax and Obamacare tax due). On the other hand, she benefits from the lower tax brackets in 2018 compared to those in 2017. Overall the 2017 tax law reduced Warren's taxes by about $2,713 (a little more than 1.1% of her total tax bill and about 0.3% of her family's gross income).
There are "above the line" adjustments to income in the amount of $59,348, there is a self-employment adjustment to correct for the self-employed paying both employee and employer FICA ($4,348) and adjustment for a retirement plan contribution in the maximum allowed amount of $55,000. Notably, she took no business expenses as deductions against her writing income. Her husband had a whopping $18 of self-employment income and took $803 of professional organization dues as a business expense.
Her self-employment income does not qualify for the pass though entity tax break created by the 2017 tax law.
Above the line deductions simply convert your self-employment income to the numbers they were be if you were an employee of someone else with the same benefits.
The marginal tax rate that Warren pays on each additional dollar of self-employment income (e.g. writing) is about 40.94% from all applicable taxes combined.