If I look at the energy start ratings of my current fridge vs. a new comparable one (same manufacturer/style, Whirlpool Cabinet-Depth side-by-side), the numbers have not improved much. The same goes for the gas water heater I replaced a month ago (previous one was 12 years old). In fact my AOSmith water heater got larger as well (20 to 22 inches across), since now they use more/thicker insulating material to improve the energy efficiency (for the same volume/capacity of the heater). The same is true for refrigerator doors where now all of them ‘appear’ thicker/deeper. What used to be a ‘cabinet-depth’ fridge (based on outside dimensions) has now LESS interior volume, because of thicker insulation. Also, from multiple observations, my conclusion is that the energy star ratings typically do not improve much before end-of-life of the device itself, except perhaps with better cooling technology. Some fridges now have a metal cold plate inside, where now it appears fridges are using ‘radiating cold plates’ vs. forced cold air for simpler models. However, those fridges typically command a much higher price (4k vs. $1500). This said, I would refrain from changing appliances just because the new ones have a slightly better Energy Star number.
However, one aspect we might be overlooking here is cleaning/maintenance. Whether it is your fridge or your AC sitting outside, those devices use heat exchangers. The fins tend to attract/collect a lot of dust, which hurts the thermal exchange and could lower your appliance’s efficiency. By how much is another (difficult to answer) question.
The one thing I would do first then, is to go and clean and remove all the dust accumulated on the
heat exchanger’s parts. Do not be afraid of using a screw driver and removing panels, but at the same time careful not to break anything or else, your wish to replace the appliance will become a must.