Your Pro plan belongs to your Newton account, not to one device. If you paid and Newton still shows Free, it's usually a short delay, a different Newton account, or an App Store or Google Play purchase that needs restoring.
Try these, in order
Give it a minute. Right after you pay, the app may say Purchase received. Your plan will update shortly. Close Settings and open it again. On desktop, click back into the Newton window. On the web, reload the Profile page.
Check which Newton account you're signed in to. On desktop, it's under Account in Settings › Profile. On a phone, it's at the top of Settings. It must be the Newton account you used when you paid.
Restore an App Store or Google Play purchase. On the phone, make sure you're signed in to the Apple ID or Google account you paid with. On iPhone and iPad, go to Settings › Upgrade to Pro and tap Restore Purchases at the bottom. On Android, go to Settings › Newton Pro and tap Restore purchases. You'll see Purchases restored. or No purchases to restore.
Paid on the web or in the desktop app? Restore can't find these, because Apple and Google didn't sell them. Sign in with the same Newton account and Pro appears on its own. On a phone, the plan then says Managed through your Newton web account.
Still Free? Contact us. In the phone apps, go to Settings › Help & Support › Chat with support. On desktop, click the Help button, then Contact us. Tell us where you paid and the email address on your receipt.
Good to know
Restore Purchases only brings back App Store and Google Play purchases.
Once Pro shows on one device, it shows on every device signed in to the same Newton account.