Voicemail

VoiceMail is carrier specific feature. All your VoiceMail messages are stored in carrier's server and that is full. Emptying iPhone will not serve the purpose

Contact the carrier

Or do the following:

1. Tap Voicemail, then tap a message.
2. Do any of the following:

• Play the message: Tap .
  • Messages are saved until you delete them or your carrier erases them.
  • Share the message: Tap .
• Delete the message: Tap Delete.
  • Note: In some regions, deleted messages may be permanently erased by your carrier. Your voice messages may also be deleted if you change your SIM card.

To recover a deleted message, tap Deleted Messages, tap the message, then tap Undelete.

Check your voicemail on iPhone - Apple Support

https://support.apple.com/guide/iphone/check-voicemail-iph3c99490e/ios

Check with your carrier on this as voicemail is managed by them.