@fixianovic welcome to the Atlassian developer community.
Given my response here:
I recommend using OAuth 2.0 and cloudid
as your “identifier of the specific jira cloud instance”. To be clear, site is not always 1:1 with company. For example, Atlassian has a handful of Jira sites in production use (and maybe 1000s in use by people and teams). As explained in that post, your client obtains that cloudid
by using the OAuth access token with this endpoint:
https://api.atlassian.com/oauth/token/accessible-resources