Can I quit to the launcher to choose another campaign?

To choose another campaign you must first quit the game and relaunch, please see:

iOS: https://support.apple.com/HT201330
Android: https://support.google.com/android/answer/9079646

On relaunching the game you will see the Campaign Launcher, where you can select a different campaign.

It is not possible to return to the Campaign Launcher from in-game due to operating system restrictions that prevent an app relaunch without a user manually closing the app.