Does Apple provide any APIs that we can use to send blue imessages or sms on their sms app? Barring Apple Messages for Business? Or are all such APIs private and only choice is to rely on services like Twilio, Telnyx, LoopMessage, SendBlue etc?
No such API. There used to be applescript automation support in iMessage on osx but that was quickly closed.You might be interested in reading https://neosmart.net/blog/imessage-for-windows/
There's also the recently reverse-engineered beeper which directly talks to apple's servers. But it's unreliable.