If you have to resort to json_query, you might as well create real loops. Below is the playbook I used to explore your data. I left in some experiments that helped me along the way. Perhaps something here will be useful to you. I added another element to your epg_bd_list to cover the single element case.
---
- name: json_query playground
hosts: localhost
gather_facts: no
vars:
application_profiles:
- app_desc: ""
app_name: NCS_Net_inf
epg_name:
- SPAN-destination-analysis
- infra_auth_servers
- netinf_test_servers
- paaa-infra-mgt
- vl2003
- app_desc: "dept: MedIT"
app_name: faculty_of_medicine
epg_name:
- medit_jump_server
- app_desc: ""
app_name: dc_qa_app_fe
epg_name:
- vl3800
epg_bd_list:
- fvAEPg:
attributes:
name: SPAN-destination-analysis
nameAlias: vl2022
- fvAEPg:
attributes:
name: vl72
nameAlias: Bone_Centre
- fvAEPg:
attributes:
name: medit_jump_server
nameAlias: Jumpin_Jiminy
tasks:
- name: Explorations of ways to examine epg_bd_list
debug:
msg:
- "aaa {{ epg_bd_list | map(attribute='fvAEPg') }}"
- "bbb {{ epg_bd_list | map(attribute='fvAEPg.attributes.name') }}"
- "ccc {{ epg_bd_list | map('dict2items') }}"
- "ddd {{ epg_bd_list | map('dict2items') | flatten | map(attribute='value.attributes.name') }}"
- name: isolate the app_name from application_profiles
debug:
msg:
- "aaa {{ application_profiles | map(attribute='app_name') }}"
- name: Uses product of epg_bd_lst.attributes.name and application_profiles to get matching app_names
debug:
msg:
- |
{% set app_names=[] %}
{% for app in application_profiles | product(epg_bd_list| map('dict2items') | flatten | map(attribute='value.attributes.name')) %}
{% if app[1] in app[0]['epg_name'] %}
{% set _ = app_names.append( app[0]['app_name'] ) %}
{% endif %}
{% endfor %}
{{ app_names }}
# - name: Would this ever be handy? Maybe
# debug:
# msg: "{{ item }}: {{ application_profiles | map(attribute='epg_name') }}"
# loop: "{{ epg_bd_list | map('dict2items') | flatten | map(attribute='value.attributes.name') }}"
#
# - name: How about this?
# debug:
# msg: "{{ application_profiles | map(attribute='epg_name') | map('select', 'in', item) }}"
# loop: "{{ epg_bd_list | map('dict2items') | flatten | map(attribute='value.attributes.name') }}"