Don’t forget to change your cell phone voicemail if you decide to use call-forwarding, and consider updating the phone number in your email signature while working remotely.
There is a possible chance that your WiFi is the reason that you are unable to set up your greetings for voicemail. Many users solved their problem by changing their network from WiFi to Cellular data. Your carrier provides the cellular data and that can be a better choice for voicemail settings.

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.
iMazing's Voicemail view includes a Transcript column. It features transcriptions of the voice messages as done by iOS. However, transcription is only available if the voice of the person leaving the voicemail is clear and in the same language as your iPhone's. Transcripts availability also depends on your carrier.