Wow, it's been a long time since I've had to change my phone number. Back then I would have done the same thing you did and send a mass text to my friends and family. People weren't as guarded back then, so they just accepted it and changed my registered number.

But if I were to do it now, I wouldn't even send a single one. I haven't called or texted any friend or family via mobile in ages. We mostly do our calls and messages over FB messenger. The OTP setup and 2FA will be a big hassle though.