The ansible documentation clearly states that fetch, fetches a file, not a list of files. Although one can program an application to deal with both a scalar and a sequence loaded from a YAML document, that is not automatic and would almost certainly have been reflected in the documentation.

Since you already have a sequence at a higher level, just extend that.

- name: Register env Type
  shell: facter configured_setup
  register: setup

- name: transparency tasks
  shell: {{some_script}} -t -a {{hosts}} -i {{inventory_hostname}}
  register: test
  when: setup.stdout == "something"

- name: fetch group_vars
  fetch:
    src: { "{{ item }}", when: setup.stdout == "something" }
    dest: "{{group_vars}}"
    flat: yes
  with_items:
    - "{{ test.stdout_lines[0] }}"
    - "{{ test.stdout_lines[1] }}"

- name: fetch group_vars2
  fetch:
    src: { filename, when setup.stdout =="something else" }
    dest: "{{group_vars}}"
    flat: yes
  with_items:
    - "{{ test.stdout_lines[0] }}"
    - "{{ test.stdout_lines[1] }}"

You might be able to reduce the repetitiveness somewhat by using YAML's anchor and merge:

- name: Register env Type
  shell: facter configured_setup
  register: setup

- name: transparency tasks
  shell: {{some_script}} -t -a {{hosts}} -i {{inventory_hostname}}
  register: test
  when: setup.stdout == "something"

- &fetchtask
  name: fetch group_vars
  fetch: &fetchsrc
    src: { "{{ item }}", when: setup.stdout == "something" }
    dest: "{{group_vars}}"
    flat: yes
  with_items:
    - "{{ test.stdout_lines[0] }}"
    - "{{ test.stdout_lines[1] }}"

- <<: *fetchtask
  name: fetch group_vars2
  fetch:
    <<: *fetchsrc
    src: { filename, when setup.stdout =="something else" }

Ansible probably expands the {{...}} before handing the document to the YAML parser, otherwise the value for shell in the "transparency task" would throw an error. But you should probably still quote that like you do with the value for dest

Use with_items instead of with_nested.

api_server_public_names is a list and cannot be used directly in the lookup. You will need to loop over the variable:

    - name: Validate DNS record lookup
      debug: msg="{{ lookup('dig', '{{ item }}' )}}"
      vars:
        dns_response: "{{ lookup('dig', '{{ item }}' )}}"
      failed_when: not dns_response
      loop: "{{ api_server_public_names }}"

Note however that your failed_when will not work as expected. You may need to do something similar to failed_when: dns_response == "NXDOMAIN"

The problem was the - dash in front of the "{{ user }}":

loop:
  - "{{ user }}"

Needs to be :

loop: "{{ user }}"

item.bgp.site is actually i of your outer loop.

Try: {% for b in i.neighbor.peer_ip %}