No. Slow Time Club has no accounts, so there's no email, password or login.
How we tell you apart
The first time you open Slow Time Club, your phone makes a random User ID for you out of letters and numbers. It isn't your email or phone number. If you contact us, this ID is how we find your purchase and help you. To copy it, open Profile (the star icon at the top left of Home), then tap Help and Legal → User ID.
Your subscription
Your subscription belongs to your Apple ID. On a new iPhone or after reinstalling, sign in with the same Apple ID and restore your purchase from the plans screen.
Your blocks and settings
Your Quick Blocks, Focus Sessions, App Limits and folders are saved on your phone only. With no account, they don't follow you to a new phone, so you'll set them up again there. A few settings, like your name and break length, are backed up to your own iCloud and can come back when you reinstall.