Lets say we want to change the backupserver2’s ip address, we do not want to
update all the inventory files, but want to have 1 definintion of
backupserver2 that is shared, so we can update it from 1 spot, for example
with host_vars.

If backupserver-1 and backupserver-2 are names, not ip addresses, the syntax you suggest is close but not correct; you would want tomsething like this in inventory 1:

all:
  hosts:
    backupserver:
      ansible_host: backupserver-1

And in inventory 2:

all:
  hosts:
    backupserver:
      ansible_host: backupserver-2

Etc.

If you are using an ip address (why are you doing that?), you can take advantage of the fact that your “inventory file” can actually be multiple files. Put the entry for the backup servers in separate files. That is, create backupserver1.yaml with:

all:
  hosts:
    backupserver:
      ansible_host: backupserver-1

Now you can run ansible like this:

ansible-playbook playbook.yaml -i inventory1.yaml -i backupserver1.yaml

Or if you’re working with inventory 2 instead:

ansible-playbook playbook.yaml -i inventory2.yaml -i backupserver2.yaml

In either case, if the address of backupserver1 changes, you only need to update the value in one place, and similarly for your other servers.

Alternately, if your only interaction with the backup server is via delegation, then there is potentially a much simpler solution. Just put all the backup servers in one inventory file:

backupservers:
  hosts:
    backupserver1:
    backupserver2:

Set an inventory variable to identify the appropriate backup server for that inventory, e.g. in inventory1.yaml:

servers:
  hosts:
    node0:
    node1:
  vars:
    backupserver: backupserver1

In your playbook, using the variable in your delegate_to option:

- hosts: servers
  tasks:
  - name: mumble backup server mumble
    delegate_to: "{{ backupserver }}"
    command: date

And then always include your “target” inventory and your backupservers inventory:

ansible-playbook playbook.yaml -i inventory1.yaml -i backupservers.yaml

Merge all inventory files. For example,

shell> cat hosts
backupserver_1 ansible_host=10.1.0.61 ansible_user=admin
backupserver_2 ansible_host=10.1.0.62 ansible_user=admin

[inventory_1]
host_1a
host_1b

[inventory_2]
host_2a
host_2b

[inventory_3]
host_3a
host_3b

[inventory_4]
host_4a
host_4b

and declare the logic in group_vars/all

shell> cat group_vars/all
backupservers:
  inventory_1: backupserver_1
  inventory_2: backupserver_2
  inventory_3: backupserver_2
  inventory_4: backupserver_1

backupserver: |
  {% for k,v in backupservers.items() %}
  {% if inventory_hostname in k %}
  {{ v }}
  {% endif %}

Then, given the playbook for testing

shell> cat pb.yml 
- hosts: all

  tasks:

    - debug:
        var: backupserver

    - command: hostname
      register: out
      delegate_to: "{{ backupserver }}"

    - debug:
        var: out.stdout

Limit the inventory on the command line

shell> ansible-playbook pb.yml -l inventory_3

PLAY [all] **********************************************************************************************************

TASK [debug] ********************************************************************************************************
ok: [host_3a] => 
  backupserver: backupserver_2
ok: [host_3b] => 
  backupserver: backupserver_2

TASK [command] ******************************************************************************************************
changed: [host_3b -> backupserver_2(10.1.0.62)]
changed: [host_3a -> backupserver_2(10.1.0.62)]

TASK [debug] ********************************************************************************************************
ok: [host_3a] => 
  out.stdout: test_12
ok: [host_3b] => 
  out.stdout: test_12

PLAY RECAP **********************************************************************************************************
host_3a                    : ok=3    changed=1    unreachable=0    failed=0    skipped=0    rescued=0    ignored=0   
host_3b                    : ok=3    changed=1    unreachable=0    failed=0    skipped=0    rescued=0    ignored=0   

Note: Add a pretask block to make sure a host is a member of a single group

  pre_tasks:

    - name: Any host can be a member of a single group only
      when: group_names | length > 1
      block:

        - debug:
            msg: >
              [ERR] Any host can be a single group member only.
              {{ inventory_hostname }} is a member of groups: {{ group_names | join(',') }}.
              End of host.

        - meta: end_host