Research Methods affects legendary rank 4 and upgrade costs.
Title. Research Methods affects the X-tech and credit costs of some of the new upgrades. Namely, those that use upgrade modules and legendary rank 4 will be affected, because these use normal crafting records with listed costs.
Rolling legendary effects 1-3 and upgrading tiers do not have their costs reduced by taking Research Methods. Those have their costs hard-coded. They're just not exposed in a meaningful way, so even with modding* I couldn't change this behavior. Good for people to know, at least.
* Setting a cost on these records does nothing. There also is no quest or script that references them. They're activated by a default object, and those are all quite hard-coded in their effects. There really is nothing exposed for us to edit here.