How to fuse correctly GPS for localization?

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I'm not an expert on this subject, but my understanding is that , in general, it "complicates" getting to a final estimated pose by requiring extra matrix multiplies. Don't forget that in a good implementation, the covariance also needs to be transformed.

What do you mean in the gps frame? You mean frame or latitude-longitude?

Your gps data comes in a gps_frame in latitude, longitude and height. This data is transformed from lat-long to utm. Then from utm to map if a datum is available. In this way you have the pose of the GPS device in reference to the map frame. After, navsat uses the tf tree to look the transform between gps frame_id and base_link in order to output /odometry/gps topic which is the pose of the robot in the map frame. The ekf listens to this topic in order to estimate the final pose.

What you want is the final estimated pose by the ekf from the gps frame in reference to the map frame?