>
starts a block scalar, in which you do not need to escape anything at all (and there are no escape sequences processed). So assuming you want single quotes around your JSON-like value, just do:
- name: Set environment variable
command: >
export EXTRA_CONFIG='{"client": {"subscriptions": ["DIND-Worker"], "cluster": "internal"}}'
Edit: Also be aware that a folded scalar by default includes a trailing newline character. If you do not want to have this, just use >-
instead of >
.