Welcome to Android Central! If you edit a contact, does it tell you which account it's associated with (e.g., your Google account, your Samsung account, or the local Phone account)?
In the Contacts app of my Galaxy A32 5G, there's no default storage location option. Whenever I create a new contact, I can select which account it goes to by tapping the dropdown menu at the upper left (which shows "Phone" by default).
If you look in your Settings >> Apps menu, find and open the Contacts app entry, and look in the app's Permissions there should be options for things like Phone, Storage, etc. Is the the Storage option enabled?
I have the same problem. I trying to set outlook.com as my default storage location for contacts. However I do not even see a "Default contact location". Under the synch option I see only Gmail and not my outlook.com email. I have a Samsung Note10+ running Android 12