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I had no idea the efficient fell off a cliff when it's raining!

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6% is quite a bit of buffer. I wouldn’t have panicked at that. I’ve been as low as 1%. As others have said, wind and raid can definitely affect efficiency. Slowing down makes a big difference. If using the route planner in the car, it would state to slow down to reach destination or give a warning it couldn’t make it based on conditions changing.
The Trip tab of the Energy consumption screen (the last one) uses real time energy usage and shows both the "all clear/all as expected" SOC at arrival, as well as the "adjusted" state of charge at arrival based on the actual trip progress so far. In cases like rain, you can see the expected and current data projection curves start to diverge. And as other mentioned, the car suggesting you to charge or to lower your speed (latter is a yellow warning above the turn by turn instructions), you will be wise to adhere to these.

As you correctly pointed out, the effect of rain and other environmental factors (wind, temperature) is the same if expressed in additional energy needed to overcome them regardless if EV or ICE car (may actually be a bit less for EVs as they have better aerodynamics). However an EV is so much more efficient then an ICE car, that as a percentage of energy needed to move the car for a mile, the environmental factors' overhead can be almost comparable to the normally needed energy.

Some random and approximate numbers example. Say overcoming rain (displacing water when tires run over it, etc. ) takes extra 100wh/mile (equivalent to a consumption of 337mpg). Lets say an EV needs 250wh/mi in normal conditions. This is extra 40% consumption (100/250). A relatively efficient ICE vehicle with 30mpg is equivalent to consumption of about 1150wh/mi. A 20mpg car is equivalent to about 1685wh/mi. In the same rain, the extra 100wh/mi overhead would only change things by 8.5% (100/1150) or 6% (100/1685). So most people have no way to notice that impact in an ICE vehicle. But it is very noticeable in an EV.

Slowing down is an easy (if annoying when rushing to a family dinner) tactic to reduce your battery usage.

Again, some rough but appropriately accurate numbers. Due to the non-linear air resistance, driving at 65mph is 8-10% more energy efficient then 70mph. Difference in % consumption is more when you have no aero covers for example as air drag increases even fasterwith speed in such case.

Graph below is from some other post here (note the scale is wh/km and km/h, not wh/mile and mph) .

I tried to take a pic of the appropriate data whenever I plugged in. The "avg. energy since last charge" numbers I recorded were: 242, 228, 231, then the dreaded 390 in the rain, 339 after a stop to look through the map, 349 to the SC in Lebanon IN, then 245 for the rest of the trip home. Then 222 for a local drive and 265 on an admittedly hotdoggin' race back to return the car in time. Big fun in busy, high speed interstate traffic. See a spot in traffic ahead? No problem, just point and shoot; you're there.

But anyway, my concern remains. Well, at least my wife's (and thus mine): how does the route planner take weather into account? Is there a connection to a weather station or something? Sounds kind of fantastical I know, but with Tesla, who knows!
Tesla's navigation takes a lot of things into account, including rain, wind, elevation changes, tire pressure, driving speed history of driver, number of passengers (in two ways, both the effect of the additional weight and the effect on the HVAC drain), it even takes into account the draw from devices plugged into the USB ports. Use the nav to plan your trip and take its advice on where to stop and how long to charge at each stop.
No doubt Rain will cause a hit. May have been more than just that in your case could have had Rain + any number of Wind, Elevation Gain, more use of climate/defogging, higher highway speeds, etc...
Is no doubt an unfortunate aspect of owning an EV. I consider it more as an inconvenience to be aware of than a major disappointment though.

The good thing is due to an in-app update a few years back now the car's computer will factor these into the equation which is why it told you to stop at the earlier Super Charger location even though purely based on mileage you should not have needed to. That is the real lesson here ; listen to the car next time.
That did not used to be the case (that the car calculations adjust based on current conditions).