updating one field in one table which create a new row in another

Hi folks, Pretty new to back end development in general and Laravel. I am hoping you guys can help me with this issue.

When i update a field in row in one table i would also like to create a row in another table in one swoop.

I have a patient appointment table with a field for a doctor_id, the idea is that the doctor can choose appointments. So when a doctor chooses the appointment i want to update that empty doctor_id field in the appointment table and subsequently create a new Chat Model so the doctor and patient can chat.

I am a little confused on what the best practice to do this? should it be a PUT HTTP Request or a POST HTTP?

here is what i have so far:

public function doctorTake($id){
    $appointment = Appointment::find($id);

    if(Auth::guard('doctor')->user()->id && !$appointment->doctor_id) {

        $appointment->doctor_id = Auth::guard('doctor')->user()->id;
        $appointment->save();

		$chat = new Chat;
		$chat->doctor_id = Auth::guard('doctor')->user()->id;
		$chat->appointment_id = $appointment->id;
		$chat->patient_id = $appointment->patient_id
		$chat->save();
        $response = ['appointment' => $appointment];

        return response($response, 201);

    }else{

        return response([
            'message' => 'Access denied, you do not have the permission.'
        ], 403);
    }
}

Route::put('/doctor/open-appointments/{id}/take', [App\Http\Controllers\API\AppointmentController::class, 'doctorTake']);