How to copy/backup folders from broken linux system

My system got messed up after an ongoing update was interrupted due to powercut and is not booting even after trying many fixes.

I decided to do fresh installation of manjaro.

I can access my files booting through LIVE USB.
I was hoping if there is a way I can backup/copy files and folders(for eg. installed icon pack, themes, /home, /opt) so that i can put them back after new installation and save myself from configuring it again.
i’m new to the linux