Sony has an entire studio, SN Systems, which does nothing but make game dev tools like compilers and profilers for other studios to use.
Everything we've seen and heard indicates the Sony SOC will be notably smaller, let's estimate by 20%. If the Series X SOC costs $175, that'd be a savings of $35 at least. PS5 uses 8 2GB RAM chips, whereas XSX uses 6 plus 4 more of half-capacity. That'd probably be a difference of about $15. Sony's lower-sized SSD uses more NAND chips, but of much lower capacity. For sake of argument let's assume that this, and every other aspect of the consoles, is a wash on cost. That's pretty unlikely--Sony still have other areas where they can be more thrifty--but let's assume the worst. That's already a $50 difference on BOM alone.
But there's another differentiator you didn't account for, and that's the presence of Lockhart. Microsoft's low-end machine has to be very low cost, about $200 less than Series X. But the only difference is an SOC 20% smaller than PS5, and two fewer chips of RAM. If this same gap can't even add up to $50 between PS5 and XSX, how can it be more than $50 between PS5 and XSS? But then there's only a $100 gap between the two Microsoft products. In order to have a low shelf price, Lockhart will likely need to take a big loss per console. Which then means Series X needs to take much less of a loss, or better, to make up for it.
Thus, a PS5 with only a $50 difference in BOM below XSX might end up $100 less on MSRP. This is far from guaranteed, but it's clearly a live possibility.