How to start a system managed ConnectionService from the default Caller App

Question

I'm implementing a system-managed ConnectionService. My app has it's own contact list. It registers a PhoneAccount which has CAPABILITY_CALL_PROVIDER capability. It starts sip calls from this contact list using TelecomManager's placeCall function and receive incoming calls using the addIncomingCall. This all shows up on the default system caller app and everything works fine until this point.

But I have some problems on the call history. My app doesn't show up as a "3P Calling App" in the call history like the screenshot I took from the documentation:

Instead I got this one below:

There are two problems here;

1. My uri format is sip:{phone}@{authority}. And it's shown without the schema part. I want to show only the phone part or a normal display name. I can't set a display name for the call history. (I guess this is not possible without importing my contacts using an "Account")
2. There isn't any call button and it says "Uninstalled app" (It's not uninstalled) If I remove the authority part from the address, the call button appears but it tries to make a normal phone call instead of a sip call.

What I want is to start my activity when user clicks a call log created by my own app.

Is this even possible to create outgoing call from the call history? If it's possible, how can I do that?