How can I check if a string exists in a file?

It’s a tricky one. the lineinfile module is specifically intended for modifying the content of a file, but you can use it for a validation check as well.

- name: find
  lineinfile: 
    dest: /etc/passwd
    line: "user"
  check_mode: yes
  register: presence
  failed_when: presence.changed

check_mode ensures it never updates the file.
register saves the variable as noted.
failed_when allows you to set the failure condition i.e. by adding the user because it was not found in the file.

There are multiple iterations of this that you can use based on what you want the behavior to be. lineinfile docs particular related to state and regexp should allow you to determine whether or not presence or absence is failure etc, or you can do the not presence.changed etc.