It is allowed to have 1 branch on the Free plan. As I can see the mv3 branch still exists in the Sources tab of your project
You’ll be able to connect the new one after you delete the existing branch from the project
Deleting the mv3 branch without affecting your source and translations is impossible.
Translations are stored in TM, so you can delete the branch from the Source tab, re-upload it with a new Github connector, and run Translation Memory pre-translations. Alternatively, you can upload the translation along with the source files during the Github setup.
The free plan has some limitations (for example, 1 branch), and the limits are applied on the Source level side, so technically, you can’t connect a new branch until the existing branch in Crowdin Sources is not deleted.
For future, you can also consider Git Actions instead of the native connector since it provides more flexibility: