You could use: GET /rest/api/2/issue/createmeta
For example, if you make a GET request to:
https://{your-jira-url}/rest/api/2/issue/createmeta
You should get a list of the projects in which the user has permission to create issues.
This assumes that:
If I am the JIRA admin, how can I make the REST request as a particular user and get back the result?
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