May i extend my AppleCare warranty for my phone?

While I have read some information about new extensions to AppleCare+ warranty, I don't believe that it can be done for a device that old. See this, About continuing your AppleCare+ coverage for iPhone, iPad, and Apple Watch - Apple Support

See the blue text in the responses you have received. Those are links to Apple Support documents, and they provide an explanation to your question. You need to check out those links to see if your device is eligible to extend your AppleCare.

Yes, it may be possible to extend an existing AppleCare+ plan.

Ref: About continuing your AppleCare+ coverage for iPhone, iPad, and Apple Watch - Apple Support

Clink on this link check your exact device’s eligibility. and see if your device is eligible.

Axel F.