My old phone says locked to owner.

Can it connect to the Internet to get the updated status from Apple?

I have to admit that I am a bit confused by the phrasing of how this works for offline removal in the document --> How to remove Activation Lock - Apple Support

To me it would imply that if a device cannot then connect to the Internet for some reason that it would not find out about its changed status.

Two directions I can think of.

1) Refer to this document for ways to contact Apple --> Choose your country or region - Official Apple Support

Select your country (also look for "other" regions), then a product. If you don't see one that handles your issue then keep experimenting with selections until you reach one that gets you a chat session or a telephone call and get the representative to redirect you.

or:

Contact Apple for support and service by telephone --> Contact Apple for support and service - Apple Support

2) Apple can completely reset a device if a person can provide sufficient evidence of valid ownership. Do this online at: Activation Lock support request - https://al-support.apple.com/#/additional-support Apple says, "Proof of ownership documentation is required," but does not detail what currently constitutes proof. Prior to this new online service Apple typically required the original receipt issued by Apple or an Apple Authorized Reseller and documented provenance (so typically it would be the original owner who does this, or a descendant with legal proof of ownership).

Apple recommends you "Keep your receipt after you buy an Apple device" --> Keep your receipt after you buy an Apple device - Apple Support

A couple of thoughts:

Check at https://appleid.apple.com/ to “double verify” that the device indeed has been removed from your AppleID.

(if not, delete it from there)

Then … make sure that the “old” phone REALLY has a working path to the internet during it’s initial setup as it DOES need to reach Apple’s activation servers.

Added: I wonder if WiFi in a [presumably] “SIM’less” iPhone even works prior to “Activation” ??? 🤔