Amazon SES migration to production

It sounds like your Amazon SES account is still in the sandbox environment, despite requesting an increase in your sending rate.

When your account is in the sandbox, there are specific restrictions:

• You can only send emails to verified email addresses and domains
• You're limited to 200 messages per 24-hour period
• You're limited to 1 message per second

The fact that you can only send to verified addresses indicates you're still in sandbox mode. To fully move out of the sandbox and into production, you need to specifically request production access, not just a sending rate increase.

To request production access:

1. Navigate to the Amazon SES Console
2. Check the "Account details" section to confirm your current status
3. Request to move out of the sandbox by following the production access request process

Once your account has been moved out of the sandbox and into production, you'll be able to send emails to any recipient, regardless of whether their address or domain is verified. However, you'll still need to verify all identities that you use as "From", "Source", "Sender", or "Return-Path" addresses.

The AWS Support team typically reviews production access requests carefully and provides an initial response within 24 hours.
Sources
Request production access (Moving out of the Amazon SES sandbox) - Amazon Simple Email Service
Migrating to Amazon SES from another email-sending solution - Amazon Simple Email Service
SES Email Will Not Send Out Of Organization | AWS re:Post