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.
Yeah, but isn't FB Messenger dependent upon a mobile phone number?
Nope. I have an old phone without a sim, and I can message and take calls there as long as I have internet [I mostly use it to search things or watch videos at home]. One just needs an email for the account, or the google account. One can link the mobile, but I don't think it's mandatory. There are things like viber and whatsapp that do need the mobile number though.