From your list of tools:

Jenkins and Github have apt/yum repositories you can use to install and upgrade. 

For Atlassian products, best up to date information about repositories I can found is [This ShipIt experiment](https://confluence.atlassian.com/display/DEV/ShipIt+8+-+Debian+Package+for+JIRA) and it seems unlikely to change from [this forum post](https://community.atlassian.com/t5/Bitbucket-questions/Is-it-possible-to-install-Bitbucket-with-apt-get/qaq-p/300619)

Now if you really want something automated to handle the installation and configuration of your tools, you can try a Configuration Management System like Chef/Puppet/Ansible/Salt.

For Chef I know better, there's cookbooks for Jira and Confluence maintained.  
For the rest you'll be on your own writing the bits to deploy and configure.

This means having 4 CI/CD systems (at least), two 'groups' validating each other, as a pipeline won't be able to validate and upgrade itself properly (inception). That sounds overkill in my opinion.

At the end of the day, there's no silver bullet for all and every software you may use, each will have its own particularity and way to be installed and you'll have to workaround those bits.