This should be trivially scriptable by ansible. Ideally you'd also transform your existing configuration into an ansible data structure so it can write out the complete config as that way is just more reliably - but ansible also is capable of editing stuff in place.

I'm using a structure like this:

wireguard:
  wg-mgmt:
    interface:
      address: 192.168.1.10/24
      listen_port: 34800
      private_key_file: /etc/wireguard/private.key
      passdb_entry: vpn/fi1-mgmt
    peers:
      aard_meteor:
        public_key: bmV2ZXIgZ29ubmEgZ2l2ZSB5b3UgdXAK
        allowed_ips:
          - 192.168.1.11/32
      aard_zak:
        public_key: bmV2ZXIgZ29ubmEgbGV0IHlvdSBkb3duCg==
        allowed_ips:
          - 192.168.1.12/32

To set up both server and client. I'm mostly adding other peoples systems, so I don't know the private keys, and receive the public ones from them - but if you control both it's also trivial to pull that information from the system you're generating it on, and reuse it later.

This is the template used for the wireguard configuration, this the task managing the wireguard setup.

Getting the pubkey from a private key into a variable in ansible would look something like this:

- name: dump pubkey
  shell: "wg pubkey < {{_pubkey_file}}"
  register: _wg_pubkey
  changed_when: false

- name: register pubkey
  set_fact:
    wg_pubkey: "{{_wg_pubkey.stdout}}"
  when: >
     _wg_pubkey is defined

It's then easy to dump it into a password store or something like that - if you check the repo in above links you'll see pass heavily used.