@siderea
It's possible to do this with xmpp clients and Twilio. You don't need to self host anything either, though that is also possible. wiki.soprani.ca/TwilioSetup
If you didn't want to use Twilio for some reason jmp.chat (run by the same people) might also work. You'd also probably want to message their support to let them know it's a business line, but from what you describe of human replies to customer initiated messages that shouldn't be a problem.
If an Android app is optional (or the website works fine on mobile) chatwoot is another option too. It's currently only possible to map a phone number to one xmpp account, so you'd have to share credentials/wouldn't be able to see who responded, just their response. Chatwoot does not have this limitation.