Hello,
No, Business Central does not automatically update the Standard Cost when a Production BOM is changed; standard costs are intentionally kept/frozen until they are recalculated and implemented. After changing the BOM, you can use Item Card → Production → Calc. Production Std. Cost (Single Level or All Levels), or for a controlled/bulk process use the Standard Cost Worksheet → Roll Up Standard Cost → Implement Standard Cost Changes, which can also create the required revaluation journal for existing inventory. If the requirement is to recalculate immediately whenever a BOM is certified/changed, that would require customization, but I would normally recommend a controlled periodic recalculation because changing standard cost can have inventory valuation and accounting implications.
Regards,
Oussama Sabbouh