If you’re expecting to use the FreePBX internals on your calls, then you need to use local channels for both legs of the originate. Not only will this ensure that the dialplan hooks get called, the calls will show up in CDRs, they will follow the recording rules you have set, etc.
For the outbound leg, you want to use Local/$DID@from-internal and for the inbound you would use Local/$EXT@originate-skipvm. More generally this would be Local/${dialed-digits}@${Context} where the priority is always 1.
As opposed to the way the AMI is configured above, it’s conventional to originate the call first to the local extension, ensure they answer, that the channel is up and only then dial the outbound leg of the call. This will ensure that any early media audio is not missed, and also ensures that the caller is not left with dead air if nobody is answering on the local side.
For those unfamiliar with the originate-skipvm context noted above, it’s a somewhat new context in FreePBX Core that allows you to originate to a local extension and prevent the call from being answered by the user’s voicemail, which you almost always want to avoid. When originating calls automatically, you need to anticipate whenever a call might be answered by a non-human and try to avoid that.