With this method, you don’t need a third-party app. Call the person you want to chat with, then tap the “Add Call” button on your phone’s screen. Dial your own phone number—the one you’re calling from. This will take you to your voicemail. Once your voicemail has started recording, tap the “Merge Calls” button on your screen. Now, you’ll record your phone conversation onto a voicemail message. When you’re done with the call, you can tap the share button to export it to your Mac via Airdrop, to the Voice Memos app, or transfer it via email or text message. The file is recorded as an M4A, so depending on what you want to do with it, you may need to convert it to MP3 before uploading it to other apps.
I have also seen this method fix voicemails that are not playing and not deleting, too. A quick reset of the voice app does wonders and takes two seconds.

Tap “Phone” on your iPhone’s “Home” screen and tap “Voicemail” to access your voice-mail settings. Tap “Greeting” and select “Default” if you wish to use the default greeting for your voice mails. Click “Custom” if you want to create a personalized greeting, and tap “Record” to say your greeting.
Website: https://www.openphone.co/blog/21-professional-voicemail-greeting-examples/