My old iPhone is still getting my calls and messages

Since you erased the old phone …

If it’s really incoming “calls” and ‘green bubble’ “texts” … it’s because it probably still has the old, still-active SIM installed.

Think of a SIM almost as a “super app” from your mobile carrier which must be physically removed.

Unless your new phone was pre-provisioned w/ an eSIM … you need to place the “old” SIM into your new phone to use your carrier’s mobile network.

It’s odd that a carrier would leave an old SIM provisioned if the line was moved to an eSIM in your 13… 🤔

Well … remove the SIM from your old phone.

That WILL stop any transmission to your old phone (and since it’s a SIM from your old carrier; destroy and dispose the SIM itself)

Your rare “flukiness” is almost certainly related to the simultaneous carrier transition - assuming that you “ported” your pre-existing number from Carrier “Old” to Carrier “New.”

It’s a quite complicated process “behind the scenes” involving SEVERAL entities with multiple electronic “handshakes” occurring between successive steps.

The “goal” is to NOT “drop” your service in the process; it appears you might have actually observed a bit of an “overlap.”

oh … and enjoy your brand new phone. 😉

How did you “erase” your old phone?

Did you follow all the numbered steps listed under “Remove your personal information from your old device” linked here:

https://support.apple.com/en-au/HT201351

Transitioning between carriers can be messy and it’s NOT an instantaneous changeover.

FWIW, “voice mail” is a “carrier” function.

I’d suggest letting it “simmer” at least thru the night before you expend too much personal energy attempting to “fix” it.

You can NEVER overcome the bureaucratic inertia of a Telco.

(It’s been honed to a “science” over the last 100 years … mostly for valid technical reasons)

They probably can’t even open a “ticket” until the transfer is “completed.”