Why isn't this command from this script run by the user specified by doas -u when this script is copied and run by an ansible playbook?

I wrote a simple playbook, open-links.yml, that is meant to run a script on one of my remote hosts:

- name: Run Bash script
  hosts: myhosts
  gather_facts: false
  vars:
    au: "j"
  tasks:
    - name: Copy and run a script that opens a link
      script: /home/{{ au }}/CS/SoftwareDevelopment/MySoftware/Bash/ansible/open-links.sh

open-links.sh is a script that is meant to open a link in a browser:

#!/usr/bin/bash


# Link to open
link_to_open="https://calendar.google.com/calendar/u/0/r "


doas -u oumaima echo "From ${0}, $(whoami): It works, doesn't it"|tee ~/debug.log
doas -u oumaima brave-browser "${link_to_open}" > /dev/null 2>&1 &
#doas -u oumaima DISPLAY=:0 brave-browser "${link_to_open}" > /dev/null 2>&1 &
#doas -u oumaima DISPLAY=:0.0 brave-browser ${link_to_open} > /dev/null 2>&1 &
#neither of these two work, whatever the value of DISPLAY

Although running ansible-playbook -u root -i inventory.ini open-links.yml gives me the following output

PLAY [Run Bash script] **********************************************************************************

TASK [Copy and run a script that opens a link] ***********************************************************
changed: [fe80::cc08:9465:8dba:15a9%wlp4s0]

PLAY RECAP **********************************************************************************************
fe80::cc08:9465:8dba:15a9%wlp4s0 : ok=1    changed=1    unreachable=0    failed=0    skipped=0    rescued=0    ignored=0

No link gets opened. The location of debug.log is /root/, and its content, ` From /root/.ansible/tmp/ansible-tmp-1702325377.165474-2513875-125933755232488/open-links.sh, root: It works, doesn't it `, both of them suggest to me that if any link does get opened, then it probably happens for root. When I am logged in with ssh to the remote host and manually run

link_to_open="https://calendar.google.com/calendar/u/0/r "
doas -u oumaima brave-browser "${link_to_open}" > /dev/null 2>&1 &

then the browser does open the link as specified for the user oumaima. I know that the link is open because the remote host is in the same room and I can seen the browser from the user account oumaima. **Forwarding to my control station of what is happening in the GUI of oumaima is not what I want and let it be outside of the scope of this question.** I just want the link to be opened. Why doesn't this happen when the script is run with ansible-playbook -u root -i inventory.ini open-links.yml I know that I could just work around that by allowing non-root logins to the remote host and running the playbook as oumaima, like so: ansible-playbook -u oumaima -i inventory.ini open-links.yml. Let such solutions be outside of the scope of this question. I'd like to fix the issue when running the playbook as root. **About the hosts**: a laptop in the same room, on the same LAN, as my control station. Ubuntu Desktop 22.04 LTS on both the control station and the remote host.