Is it routine for the Apple store tech handling a phone trade in to say he will dispose of your old sim card?

Why don't you ask them?

FYI: These are user-only forums. Apple is not here. Thank you for your understanding and support. Should you need further help: Contact Apple Customer and Support Service.

1. Apple Store Customer Service at 1-800-676-2775 or visit online Help for more information.
2. Primary support help at Contact Support.
3. To contact product and tech support:  Contacting Apple for support and service including international calling numbers.

There is nothing stored on a SIM.

It’s only purpose is to allow to connect to the cellular network.

If the SIM card in your new phone is activated and working, the old one has been deactivated.

What is it you imagine they might be trying to do?

Every time I have bought a phone at an Apple store , they have offered to swap my SIM over or activate the new one in the device. They have taken my old SIM and thrown it away.