It will need to talk to Jira over the REST API - start at https://developer.atlassian.com/cloud/jira/software/rest/intro/ - it's got docs on the calls you can make, examples, and a load of stuff about authorisation.
The bit it does not cover is "permissions in Jira are respected by the REST API" - you'll need to have a rummage through permissions in Jira. As a very simple example, if Charlie-the-coder can see projects A and B, but does not have permission to see C, then if Charlie issues a search over REST for "all open issues", the REST API will return a list of issues from projects A and B only, not C. Similarly, if Charlie tries to create an issue in C, it will fail because Charlie does not have permission to do it.
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