Settings > Apps > Messages > RCS Messaging

If it isn't there, About > Settings > General > About and tap the Carrier row. If it doesn't say RCS, the carrier doesn't support it.

Also one should note, MMS also requires carrier support and a few carriers don't support it in some countries.

There's a list of supported features for carriers worldwide at https://support.apple.com/en-gb/108048

Got it, I'll move to a country that supports RCS at my earliest convenience, and also not message anyone while I'm roaming to another carrier on vacation.

My carrier should support MMS, but I haven't yet had it work (and inbound messages to my number, like the picture of a family-member's wedding invite sent to my phone number, just silently vanish into the void)... I just kinda assumed it was working as expected since I'd heard so much about the green bubble issues.