I have a bit of experience assisting family members with this type of change (and in getting their pricey medications continued). I'd be happy to process with you through DMs once you find a few things out.

@sueinmn gave you the most important advice and that is to get your new plan's specific formulary. Do people talk to your HR department a lot about insurance? If so yours is probably a company sponsored plan (even if it's Blue Cross or some other familiar brand, it may be very specific to your company and your company may have called the shots on what it does and doesn't cover).

If your new drug formulary doesn't cover Tymlos, the insurance/pharmaceutical policy that you'll need to refer to and stand on as you advocate for yourself is "continuity of therapy" (COT). If you can let me know the name of your plan I can google and try to find PDF(s), etc. on their COT policy. Most state that if you have been on a medication for at least 90 days, your provider can arrange COT for you by filling out that form, which is a lot like a Prior Authorization request but is usually labeled a "Formulary Exception" request for reasons of COT.

You are smart to figure out your new plan's policies ahead of time so that you can get your ducks in a row and hit the ground injecting in January :-)!