I understand that you're using Jira Cloud and you want to be able to see all the repo branches in Github that are linked to a particular Jira issue.
This question has actually been asked a few times before in Community, I think the best example with a great answer is over in https://community.atlassian.com/t5/Jira-questions/API-get-branches-related-to-issue/qaq-p/1214220
Dario explains that the REST API endpoints there are technically not public and subject to change at any time. That said he does explain how this could be made to work for any REST client such as the jira-python sdk.
I hope this helps.
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