Ansible: set_fact after successful variable match in array

I have following playbook ~ # cat demo.yml:

- name: demo
  hosts: localhost
  gather_facts: no

  vars:
    set:
      task:
        type: var1
    task:
    - type: var1
    - type: var2
    - type: var3
  
  tasks:
  - debug:
      var: set

  - debug:
      var: task

  - set_fact:
      task: 
        type: "{{set.task.type if item.type is search(set.task.type|join('|')) else 'absent'}}"
    loop: "{{task}}"
  
  - debug:
      var: task

**Output:**

PLAY [demo] ************************************************************************************************************************************************************************************************

TASK [debug] ***********************************************************************************************************************************************************************************************
ok: [localhost] => {
    "set": {
        "task": {
            "type": "var1"
        }
    }
}

TASK [debug] ***********************************************************************************************************************************************************************************************
ok: [localhost] => {
    "task": [
        {
            "type": "var1"
        },
        {
            "type": "var2"
        },
        {
            "type": "var3"
        }
    ]
}

TASK [set_fact] ********************************************************************************************************************************************************************************************
ok: [localhost] => (item={'type': 'var1'})
ok: [localhost] => (item={'type': 'var2'})
ok: [localhost] => (item={'type': 'var3'})

TASK [debug] ***********************************************************************************************************************************************************************************************
ok: [localhost] => {
    "task": {
        "type": "var1"
    }
}

PLAY RECAP *************************************************************************************************************************************************************************************************
localhost                  : ok=4    changed=0    unreachable=0    failed=0    skipped=0    rescued=0    ignored=0

As you could see this works great and new value for variable task.type is set to **var1**. However the problem is when I provide set.task.type: var4 or any other variable. Than task.type is set to **var4** instead of **absent**. **Question:** How to set new value task.type: absent if set.task.type does not match any values from the array?