Example Full Path: X:\East\_Complete Downloads\[2ndfire]Haibane_Renmei[BD][1080p][Dual-Audio][AV1][10bit]\Haibane Renmei - S01E01 - Cocoon Dream of Falling from the Sky Old Home.mkv
The regex is performed on the filename, not the full path, so that approach won't work.
You can use {parent1}, {parent2}, etc. to insert the names of parent folders into the new name. So you could do that and then a second rename. Or you could use a rename script which lets you do pretty much anything, all in one go, including apply a regex to the full path: Script to perform multiple Regular Expressions