The https://marketplace.atlassian.com/apps/1211542/atlassian-rest-api-browser?hosting=server&tab=overview (currently Server only) is usable with JEMH.
JEMH has a lot of internal application REST services that are not recommended for use, we have a /public/ api section that is for external integration by REST:
Examples
atl_token is required on most calls, see most logged in pages for atlassian_token in html.
Listing profiles
prior to 3.3.36, the Profile needed to be edited and the API box checked for a profile to appear in this list, we’re relaxing that and applying specifically to the API for posting mail through a given profile.