Here is a chronological summary of what happened.

My local copy of a branch, let's call it featurebranch is fully up to date with the copy of this branch on github
On my local machine, I delete a file called test.csv.
I call "git pull origin featurebranch" on my local machine, but the test.csv does not show up on my local machine
I call "git status" and output is "Changes not staged for commit: deleted test.csv"
I call "git add test.csv"
I call "git status" and output is "Changes to be committed: deleted test.csv"
I call "git commit - m "delete test file""
I call "git pull origin featurebranch" and output is "Already up to date"

It's not up to date though. test.csv still exists on github but not on my local machine. How do I get this file back on my local machine? I assume there is something about how git works that I do not realize. Thank you for reading.
git pull is used to "sync" your branch with the latest commits in the remote repository (GitHub). It is not used to sync files.
Since featurebranch was never updated in the remote with new commits that you don't have, git pull has nothing to do - there are no new commits to fetch and sync to. Your commit is the most up-to-date version of that branch.
If you want your file back, you can either git reset <older_commit> the branch to some older commit that contained the branch. Or you can git revert <the_commit_that_deleted_the_file> the commit that deleted that file. Or you can git checkout <some_other_commit> -- test.csv to selectively restore the file from <some_other_commit> that contains the file. Or you can git checkout  or git switch to some other branch/commit to change your working directory to a commit that actually had that file.
After deleting a file from my local machine, how do I pull from github to obtain that file again?