To extract a directory from a repository and keep the history, you can use the git subtree split command to create a new branch:
git subtree split --prefix=web/modules/custom/my_module --branch=split
Created branch 'split'
17835f24069061326e9e065f076afd67434e1b2f
This will create a new branch with just the contents of the given directory.
This can be pushed to a different repository:
git push [email protected]:opdavies/new-repo.git split:main