How to get interpolated value of variable in Ansible / Jinja2

I'm trying to define Ansible variables this way:

user:
  name: First Last
  nick: '{{ vars["user"]["name"] | regex_replace("\W", "_") }}'
  email: '{{ vars["user"]["nick"] }}@example.com'

And the result email is: "{{ vars[\"user\"][\"name\"] | regex_replace(\"\\W\", \"_\") }}@example.com.

I also tried to set email like this: {{ lookup("vars", "user.nick") }}@example.com
or {{ lookup("vars", "user")["nick"] }}@example.com,
and it says An unhandled exception occurred while running the lookup plugin 'vars'.

Is there a way to get resulting variable values as:

user:
  name: First Last
  nick: First_Last
  email: First_Last@example.com

?

ansible 2.9.10, python version = 3.8.5

It's not possible cross-reference keys in a dictionary. It's necessary to declare the variables outside the dictionary. For example, the playbook

- hosts: localhost
  vars:
    my_name: First Last
    my_nick: "{{ my_name | regex_replace('\\W', '_') }}"
    user:
      name: "{{ my_name }}"
      nick: "{{ my_nick }}"
      email: "{{ my_nick }}@example.com"
  tasks:
    - debug:
        var: user

gives (abridged)

  user:
    email: First_Last@example.com
    name: First Last
    nick: First_Last

A more flexible option is to create the variables in the loop. For example, the playbook

- hosts: localhost
  vars:
    users:
      "First Last":
        domain: example.com
  tasks:
    - debug:
        msg:
          - "name: {{ name }}"
          - "nick: {{ nick }}"
          - "email: {{ email }}"
      loop: "{{ users|dict2items }}"
      vars:
        name: "{{ item.key }}"
        nick: "{{ item.key|regex_replace('\\W', '_') }}"
        email: "{{ nick ~ '@' ~ item.value.domain }}"

gives (abridged)

  msg:
  - 'name: First Last'
  - 'nick: First_Last'
  - 'email: First_Last@example.com'