Have you ever tried to use Jira as development board and Azure DevOps as repository + CI/CD Pipelines? I was wondering if it is possible to link to Jira tasks the results of Azure pipelines deployments and builds, i found this plugin but reviews say is not working properly recently.
EDIT
Using the mentioned plugins seems the right way although they are not working properly at the moment. I will try to contact the support as suggested.
According to your description, you can try to use the plugin for Azure DevOps.
Then you can use the flow: Jira -> GitHub -> Azure Pipelines CI -> Azure Pipelines CD.
For more information, you could refer to the Azure Pipelines integration with Jira Software.