"Our company used Twilio to receive and forward messages to our Slack in the past. Unfortunately, not all websites send messages to these phone numbers."
This right here is a deal-breaker. But this does remind me of a project I started at one time to make an Android app that reads SMS messages as they come in and then forwards them via Wire (or Telegram or Signal or MS Teams or Slack) allowing a "real" cell number to be used for SMS 2FA without the need to have that device in-hand at all times. The idea of sharing the SMS to Slack is another excellent idea; sharing it to a Signal/Wire/Telegram group for geo-distributed open source teams working on an idea or project would be good too.
