My old iPhone screen is broke and won’t let me sign into the phone how do I transfer all my old data to my new phone?

Use your iCloud or iTunes backup and restore the new phone with the backup. If you don’t have a backup, then you’re out of luck now that your old phone is broken.

Data that you sync to iCloud (contacts, notes, iCloud Keychain passwords, etc) should just sync to the new phone when you sign into your iCloud account.

See -> Transfer data from your previous iOS device to your new iPhone, iPad, or iPod touch - Apple Support