its not a cool off period, google just made app homepage + privacy policy url required to publish, even for a personal one user app. thats why the button is greyed out until branding is filled in.
testing mode still works but the refresh token dies after 7 days so you end up reauthing constantly, annoying as hell.
cheapest way around it if you dont wanna buy a domain is a github pages page with a dummy privacy policy and point homepage + privacy policy at it. thats enough for google to let you publish. otherwise stay in testing and eat the weekly reauth.