According to your description, your issue is related to the third party product development, which we do not support. I will provide some personal experience from the Microsoft Teams. Hope it will helpful to you.
In my experience, you can extend your Teams app with a custom tab. It allows you to serve web content that you host to your channel, group chat, and personal users. For more details about how to extend your Teams app, you can learn it from:
Some users also tried to integrate Jira with Microsoft teams tab by using the jira connector, you can view this link to know detailed steps about how to start it.
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