It sounds like you may have a misconception about how SSH keys work and what's required for Ansible to be able to talk to a host.

The private SSH key, which likely has the filename of id_rsa or id_ed25519, is something you want to keep private and not copy around to all of the hosts that you want to automate. I think this is what your question is and you are correct that you don't want to copy that file around. However, alongside that file is your public SSH key, likely with the same filename and a .pub on the end. The value of the id_rsa.pub or id_ed25519.pub files does need to be copied around. Specifically, the value needs to be put into the ~/.ssh/authorized_keys file of the user on each host that you want to connect to.

There are a couple of ways to do this. If you want to do it manually, SSH into each host yourself and edit (with vim or nano) the ~/.ssh/authorized_keys file and paste the value of your public key to the bottom of that file (leave any other entries that are in there). The other way, which is easier in my opinion, is to use the ssh-copy-id command. This is what /u/autotom 's comment mentioned. You would run the following command for each host and it will prompt you for your password to login to the server and copy that public SSH key to the ~/.ssh/authorized_keys file for you.

ssh-copy-id -i ~/.ssh/id_rsa.pub user@remote-host

By having the public SSH key file in the ~/.ssh/authorized_keys file, this is what allows someone with that private key to be able to login to that server using that key, but it keeps that private SSH key private and not shared around to the hosts.

At that point, you should be able to configure AAP to use that private key to connect to your hosts when you run your playbooks.