Sentry's API lives at https://sentry.io/api/0 (de.sentry.io for EU data). Most paths start with your organization slug.
Get a user auth token at sentry.io. Send it as Authorization: Bearer <token>. In the examples it's written {{SENTRY_TOKEN}}.
Full reference: https://docs.sentry.io/api/
curl https://sentry.io/api/0/organizations/ \
-H "Authorization: Bearer {{SENTRY_TOKEN}}"
curl https://sentry.io/api/0/organizations/{{ORG_SLUG}}/projects/ \
-H "Authorization: Bearer {{SENTRY_TOKEN}}"
query uses Sentry's search syntax.
curl "https://sentry.io/api/0/organizations/{{ORG_SLUG}}/issues/?query=is:unresolved&limit=5" \
-H "Authorization: Bearer {{SENTRY_TOKEN}}"