Deployment system to Web-servers with Web-interface. Are there ready-made solutions?

Question

Software Deployment

Now we have a self-written deployment system. By clicking on the button in the Web interface, the current trunk is taken, a branch with the next version number is made from it, and on the server, in the document root, a switch is made to the newly created branch.
Also in the same interface there is a list of previous releases and you can always choose what to roll back to in case of problems.
At the moment we have SVN. We are planning to migrate to GIT. Accordingly, you still have to shake up the deployment system. What do you recommend looking at? As noted in the topic - I want to have a Web interface, and not just a command line.
In the vastness of Google Yandex they advise: capistrano, fabric, Mina, Vlad the Deployer...
At superficial inspection - everywhere only the command line. Maybe there are projects for these projects that offer a Web interface based on the command line?

Answer 1

Maybe I'll be stupid now :) But Puppet and Ansible are server configuration management systems. It seems like deployment for them is not a core task.
And Jenkins (or, for example, TeamCity) is CI. We have not grown up to him yet :( Again, the deployment is not his profile.

Answer 2

Travis-CI see: Travis-CI Docs