how to switch default hosting domain with secondary (firebase provided) one?

[babalift]

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Hello and thanks for your help!
I already failed with the github action deploys to firebase. So I decided to keep do a step back for troubleshooting and learning.

I have a project in the firebase console called "babalift". in the hosting panel I have 2 sites/domains : babalift.web.app and  babalift-417115.web.app. The latter and uglier is the default one, so when I deploy from the terminal that is where the index file is going to be. I would like to have the site deployed to the shorter domain "babalift.web.app". From the hosting panel i could delete the shorter one but not the default one. I wish it was the opposite. I searched and asked AI but all I get are wrong commands to terminal and not properly set up json configs...
Thanks for your baby-steps advices!