RegEx: Can you rename a File with a part of the Parent Folder name?

In Advanced Rename, I'm trying to use RegEx to capture part of the Parent Name and append it to the Original File Name.

Old Name:
^.*\\(\[.*?\]).[^\[]+(\[.*\])\\.*
New Name:
\1 {name} \2

It seems to work on RegEx101.com:
https://regex101.com/r/eQCN0U/1

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

Desired Result:
[2ndfire] Haibane Renmei - S01E01 - Cocoon Dream [BD][1080p][Dual-Audio][AV1][10bit].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

What about this example? It looks like it's possible or am I wrong?
https://resource.dopus.com/t/rename-using-the-first-num-characters-from-the-parent-name/36246

That's just using characters from the filename.

Okay, I see now. The first few numbers of the folder are also in the file so the RegEx just pulls them from the file.

Thanks!