Make copy of repo
git clone dirtySourceRepo newSourceRepo
OR clone from actual git repo and prevent push
git remote set-url --push origin no_push
Make sure to checkout the correct branch before the next step.
Cloning from another local directory allows you to easily start over if you make a mistake and also prevents you from accidentally pushing upstream.
use github.com/newren/git-filter-repo to filter down to the folder you actually care about
git filter-repo --subdirect-filter /subdirectory/I/want/to/extract --to-subdirectory-filter the/new/folder/I/want/it/in
This moves the subdirectory to the root of your repo. You can use different variations of this if you want to. You can omit
--to-subdirectory-filter if you want the contents of the folder to be in the root of the repo.
In destination repo (which can be a new empty repo or an existing one), set a new remote to the freshly filtered source repo.
git remote add source ../newSourceRepo
Make a new branch to put the stuff into
git checkout -b newBranch
Then pull in the content from the source repo:
git pull source master --allow-unrelated-histories