Anyone whose been through this, do you have any tips for how to manage this efficiently so that I don’t suddenly lose access to critical services because of a phone number change?
If you do not have both numbers then you may have to open a support case and may have to send in copies of your state ID and other documents. For brick-and-mortar businesses, just walk in and have an employee help you. This is important with banks as sometimes your number may be in sub-systems that the user portal does not update.
Enable call forwarding on the old line to your new number so that if they call to verify you, you get the voice call. That won't help with SMS text messages however may be useful if they call to verify your number change. For most U.S. providers this is *72 1 10 digit number but I would still look that up. *73 to cancel unconditional call forwarding in most providers in the US at least.