Twilio is pretty great but for this use case using Google Voice is a lot simpler (assuming its available in your country)

I recently did this for a firm that is fully remote now during pandemic. They had non voip line for main number. Set the office phone to FW to a GV number and put GV in DND so it goes straight to voicemail which was what they wanted. Then setup GV to send voicemail to email and gmail to forward to slack channel using the basic slack email integration app.

All in all very easy to setup in 20 min or less and get transcribed VM in slack channel with link to play the message as well.